a new method for adding a parameter to a family of distributions with application to the exponential and weibull families summary a new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two parameter extension of the exponential distribution which may serve as a competitor to such commonly used two parameter families of life distributions as the weibull gamma and lognormal distributions in addition the general method is applied to yield a new three parameter weibull distribution families expanded using the method introduced here have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution again in the family bivariate versions are also considered

rationality transitivity and contraposition abstract the purpose of this note is to compare the rule of rational monotonicity proposed in 3 and different rules expressing some weak forms of transitivity and contraposition we present four weak forms of transitivity that in preferential logic are equivalent to rational monotonicity and a weak form of contraposition that is strictly weaker than rational monotonicity but equivalent to it in the presence of disjunctive rationality

double faced rough sets and rough communication this paper shows that each rough set can be evaluated from two different aspects which may be considered as two facets of rough sets one refers to the conceptual meaning of each rough set e g we say that the concept of lion is included in the concept of animal and the concept of animal has a higher order of inclusion than the concept of lion the second one refers to the amount of knowledge that each rough set exhibits e g a zoologist may consider a more informative rough set for the concept of lion he considers more kinds of lions in his set than a rough set which proposed by a nonspecialist person so the first facet views the theory of rough set as an extension of the classical set theory in terms of the three valued logic which is a proper tool of reasoning and decision making based on a solitary source of information the second facet concerns the ability of rough set theory to knowledge manipulation and reduction among several information sources such that we do not care the soundness or falsity of the available information we show that the second facet is the salient characteristic of rough sets which has the capability of being extended more in new application areas as a result we present a new extension of rough sets called rough communication as a proper tool of dealing with several information sources at the end we refer to some interesting mathematical symmetries between two facets which may be used to propose new extensions

the odd lomax generator of distributions properties estimation and applications abstract we introduce a new family of continuous distributions called the odd lomax g class and provide four special models we derive explicit expressions for the ordinary and incomplete moments generating function renyi entropy order statistics and probability weighted moments the maximum likelihood and least squares methods are used to estimate the model parameters the flexibility of the proposed family is illustrated by means of two applications to real data sets

uniform semantic treatment of default and autoepistemic logics we revisit the issue of epistemological and semantic foundations for autoepistemic and default logics two leading formalisms in nonmonotonic reasoning we develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs for each logic we introduce a monotone operator on the lattice of belief pairs we then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator or as fixpoints of certain closely related operators our approach elucidates fundamental constructive principles in which agents form their belief sets and leads to approximation semantics for autoepistemic and default logics it also allows us to establish a precise one to one correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic the correspondence exploits the modal interpretation of a default proposed by konolige our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic a result that has been long anticipated at the same time they explain the source of the difficulty to formally relate the semantics of default extensions by reiter and autoepistemic expansions by moore these two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics

multivariate elliptically contoured distributions for repeated measurements summary the multivariate power exponential distribution a member of the multivariate elliptically contoured family provides a useful generalization of the multivariate normal distribution for the modeling of repeated measurements both light and heavy tailed distributions are included the covariance matrix retains its interpretation so that it can easily be structured for serial dependence and several levels of variance components a crossover trial on insulin applied to rabbits with a series of repeated measurements within each period is analyzed by means of this distribution using autocorrelation and two levels of variance components

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

belief functions on distributive lattices the dempster shafer theory of belief functions is an important approach to deal with uncertainty in ai in the theory belief functions are defined on boolean algebras of events in many applications of belief functions in real world problems however the objects that we manipulate is no more a boolean algebra but a distributive lattice in this paper we employ birkhoff s representation theorem for finite distributive lattices to extend the dempster shafer theory to the setting of distributive lattices which has a mathematical theory as attractive as in that of boolean algebras moreover we use this more general theory to provide a framework for reasoning about belief functions in a deductive approach on non classical formalisms which assume a setting of distributive lattices as an illustration of this approach we investigate the theory of belief functions for a simple epistemic logic the first degree entailment fragment of relevance logic r by providing an axiomatization for reasoning about belief functions for this logic and by showing that the complexity of the satisfiability problem of a belief formula with respect to the class of the corresponding dempster shafer structures is np complete

paraconsistent disjunctive deductive databases abstract databases and knowledge bases could be inconsistent in many ways the semantical characterization of deductive databases that contain disjunctive or indefinite information has been investigated by minker and his co workers 1982 1987 1988 and by henschen and his co workers 1985 1988 in both cases there is one salient feature the databases are assumed to consist of sentences of the form a 1 a n b 1 b m where each a i and each b j is an atom and n 1 thus the database is implicitly assumed to be consistent it is easy to construct a model for any set of such formulas what we study here is a method for reasoning about such databases when they are not necessarily consistent intuitively this occurs when the a i s are restricted not just to atomic formulas but also to negated atoms we use the device of annotated atoms introduced by blair and subrahmanian 1987 1988 to achieve this effect our semantics is closely related to the existing work of newton da costa 1974 1987 whose pioneering work on paraconsistency provides the semantical basis for our formal development

a general class of parametric models for recurrent event data the general class of models proposed by pena and hollander for recurrent event data is considered under a fully parametric specification of the baseline hazard rate function and under the two cases where the model does and does not incorporate frailty components estimators of model parameters are presented and their finite and asymptotic properties are ascertained for the asymptotic properties the results of borgan concerning maximum likelihood estimators in counting process models are used to obtain weak convergence to gaussian distributions of estimators however the required regularity conditions are reformulated into conditions involving gap times which make it more feasible to obtain explicit theoretical expressions of asymptotic covariances the procedures are applied to fit the general class of models with a parametric baseline hazard rate function to a dataset on hydraulic subsystems of load haul dump machines in mining

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

modelling irregularly sampled profiles of non negative dog triglyceride responses under different distributional assumptions general methodology for modelling series of non negative data observed at unequally spaced times is developed the parameterization enables both the importance of the serial association as well the order of this dependence to be expressed an example is given where the effects of three fibre based diets on dog triglyceride profiles are analysed and compared many different types of models based on common distributions such as the normal exponential gamma weibull and log normal observations are presented comparison of possibly non nested models fitted on the same data set is made using the akaike criterion

recursive clipping and filtering with bounded distortion for papr reduction repeated clipping and filtering rcf is a simple method for reducing the peak to average power ratio papr of the signal in the orthogonal frequency division modulation ofdm system we propose to modify rcf by limiting the distortion on each tone of the ofdm so that both low papr and low error can be achieved

nonparametric estimation with recurrent event data the problem of nonparametric estimation for the distribution function governing the time to occurrence of a recurrent event in the presence of censoring is considered we derive nelson aalen and kaplan meier type estimators for the distribution function and establish their respective finite sample and asymptotic properties we allow for random observation periods for each subject under study and explicitly account for the informative sum quota nature of the data accrual scheme these allowances complicate technical matters considerably and in particular invalidate the direct use of martingale methods consistency and weak convergence of our estimators are obtained by extending an approach due to sellke who considered a single renewal process i e recurrent events on a single subject observed over an infinite time period a useful feature of the present analysis is that strong parallels are drawn to the usual single event setting providing a natural route toward developing extensions that involve

on the analysis of life tables for dependent observations applying methods assuming independence when observations are positively correlated means that confidence intervals become too short and significance levels of statistical tests are less extreme this paper discusses elements of life table analysis based on the standard product limit estimator and a modified greenwood formula for its variance to be used for dependent observations an application from oral surgery is given erroneously assuming independence in the analysis of a life table could have serious consequences it is demonstrated in a simulation study that the confidence levels can be much too low the proposed modification of the greenwood formula for the variance of the estimated survival function most often results in confidence levels not too much below the required level using the upper bound for the variance will give conservative confidence intervals but also larger standard errors averaging individual group survival curves should only be considered for situations with large groups

statistical analysis of repeated events forming renewal processes for each of several individuals a sequence of repeated events forming a renewal process is observed up to some censoring time the object is to estimate the average interevent time over the population of individuals as well as the variation of interevent times within and between individuals medical motivation comes from gastroenterology and concerns the occurrence of certain cyclic movements in the small bowel during the fasting state two statistical models are considered one is the standard variance component model adapted to censored data and the other is a recent intensity based model with a random proportionality factor representing interindividual variation these models are applied to the motility data and their advantages are discussed the intensity based model allows simple empirical bayes estimation of the expected interevent times for an individual in the presence of censoring

on marshall olkin type distribution with effect of shock magnitude abstract in classical marshall olkin type shock models and their modifications a system of two or more components is subjected to shocks that arrive from different sources at random times and destroy the components of the system with a distinctive approach to the marshall olkin type shock model we assume that if the magnitude of the shock exceeds some predefined threshold then the component which is subjected to this shock is destroyed otherwise it survives more precisely we assume that the shock time and the magnitude of the shock are dependent random variables with given bivariate distribution this approach allows to meet requirements of many real life applications of shock models where the magnitude of shocks is an important factor that should be taken into account a new class of bivariate distributions obtained in this work involve the joint distributions of shock times and their magnitudes dependence properties of new bivariate distributions have been studied for different examples of underlying bivariate distributions of lifetimes and shock magnitudes the joint distributions of lifetimes of the components are investigated the multivariate extension of the proposed model is also discussed

a new compounding family of distributions we propose a new four parameter family of distributions by compounding the generalized gamma and power series distributions the compounding procedure is based on the work by marshall and olkin 1997 and defines 76 sub models further it includes as special models the weibull power series and exponential power series distributions some mathematical properties of the new family are studied including moments and generating function three special models are investigated in detail maximum likelihood estimation of the unknown parameters for complete sample is discussed two applications of the new models to real data are performed for illustrative purposes

the value of the four values in his well known paper how computer should think belnap 1977 argues that four valued semantics is a very suitable setting for computerized reasoning in this paper we vindicate this thesis by showing that the logical role that the four valued structure has among ginsberg s bilattices is similar to the role that the two valued algebra has among boolean algebras specifically we provide several theorems that show that the most useful bilattice valued logics can actually be characterized as four valued inference relations in addition we compare the use of three valued logics with the use of four valued logics and show that at least for the task of handling inconsistent or uncertain information the comparison is in favor of the latter

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

a top k query answering procedure for fuzzy logic programming we present a top k query answering procedure for fuzzy logic programming in which arbitrary computable functions may appear in the rule bodies to manipulate truth values the top k ranking problem i e determining the top k answers to a query becomes important as soon as the set of facts becomes quite large

performance analysis of deliberately clipped ofdm signals we analyze the performance of the clipped orthogonal frequency division multiplexing ofdm system in terms of peak power reduction capability and degradation of channel capacity the clipping is performed on the baseband ofdm signals with and without oversampling followed by the ideal low pass filter first the effect of the envelope clipping on the peak to average power ratio papr and the instantaneous power of the band limited ofdm signal is studied we then discuss the channel capacity of the oversampled and clipped ofdm signals over the additive white gaussian noise and ideally interleaved rayleigh fading channels the capacity is calculated based on the assumption that the distortion terms caused by the clipping are gaussian it is shown that the snr penalty due to the clipping can be considerably alleviated by using optimal coding and reducing the information data rate the results are justified by the simulation results using near optimal turbo codes

a new family of marshall olkin extended generalized linear exponential distribution the purpose of this paper is to introduce a new family of marshall olkin extended generalized linear exponential distribution this new family has the advantage of being capable of modeling various shapes of aging and failure criteria the proposed family includes as special cases several marshall olkin extended distributions studied in the literature such as exponential rayleigh linear failure rate and weibull among others some statistical and reliability properties of the new family are discussed and an explicit expressions for the quantiles are derived the method of the maximum likelihood estimation is used to estimate the unknown parameters in addition the asymptotic confidence intervals for the parameters are derived from the fisher information matrix finally the obtained results are validated using some real data sets and it is shown that the new family provides a better fit than some other known distributions

a general family of distributions for longitudinal dependence with special reference to event histories event histories play an increasingly important role in medical studies examples include times between recurrences of tumours as with bladder cancer and between repeated infections as with chronic granulotomous disease a general method for generating new distributions is proposed by introducing an intensity function into a density this procedure yields as special cases several distributions already proposed in the literature the families of distributions based on the pareto distribution are of particular interest for event history analysis because of their relationship to the laplace transform of a gamma distribution they can yield multivariate distributions with longitudinal serial dependence by a procedure similar to updating in the kalman filter and with uniform dependence in a similar way to copulas for longitudinal dependence several such updating procedures are proposed

modelling income data using two extensions of the exponential distribution abstract in this paper we propose two extensions of the exponential model to describe income distributions the exponential arctan eat and the composite eat lognormal models discussed in this paper preserve key properties of the exponential model including its capacity to model distributions with zero incomes this is an important feature as the presence of zeros conditions the modelling of income distributions as it rules out the possibility of using many parametric models commonly used in the literature many researchers opt for excluding the zeros from the analysis however this may not be a sensible approach especially when the number of zeros is large or if one is interested in accurately describing the lower part of the distribution we apply the eat and the eat lognormal models to study the distribution of incomes in australia for the period 2001 2012 we find that these models in general outperform the gamma and exponential models while preserving the capacity of the latter to model zeros

semantical considerations on nonmonotonic logic abstract commonsense reasoning is nonmonotonic in the sense that we often draw on the basis of partial information conclusions that we later retract when we are given more complete information some of the most interesting products of recent attempts to formalize nonmonotonic reasoning are the nonmonotonic logics of mcdermott and doyle 1 2 these logics however all have peculiarities that suggest they do not quite succeed in capturing the intuitions that prompted their development in this paper we reconstruct nonmonotonic logic as a model of an ideally rational agent s reasoning about his own beliefs for the resulting system called autoepistemic logic we define an intuitively based semantics for which we can show autoepistemic logic to be both sound and complete we then compare autoepistemic logic with the approach of mcdermott and doyle showing how it avoids the peculiarities of their nonmonotonic logic

nonparametric and semiparametric trend analysis for stratified recurrence times summary recurrent event data are frequently encountered in longitudinal follow up studies when the occurrences of multiple events are considered as the major outcomes suppose that the recurrent events are of the same type and the variable of interest is the recurrence time between successive events in many applications the distributional pattern of recurrence times can be used as an index for the progression of a disease such a distributional pattern is important for understanding the natural history of a disease or for confirming long term treatment effect in this article we discuss and define the comparability of recurrence times nonparametric and semiparametric methods are developed for testing trend of recurrence time distributions and estimating trend parameters in regression models the construction of the methods is based on comparable recurrence times from stratified data a real data example is presented to illustrate the use of methodology

bilattice logic properly displayed we introduce a proper display calculus for non distributive lattice logic which is sound complete conservative and enjoys cut elimination and subformula property properness i e closure under uniform substitution of all parametric parts in rules is the main interest and added value of the present proposal and allows for the smoothest belnap style proof of cut elimination and for the most comprehensive account of axiomatic extensions and expansions of lattice logic in a single overarching framework our proposal builds on an algebraic and order theoretic analysis of the semantic environment of lattice logic and applies the guidelines of the multi type methodology in the design of display calculi

nonmonotonic logic ii nonmonotonic modal theories tradmonal logics suffer from the monotomclty problem new axioms never mvahdate old theorems one way to get nd of this problem ts to extend traditional modal logic in the following way the operator m usually read possible is extended so that mp is true whenever p is consistent with the theory then any theorem of this form may be mvahdated if p s added as an axiom this extension results m nonmonotomc versions of the systems t 4 and 5 these systems are complete in that a theorem is provable in a theory based on one of them just if it is true m all noncommittal models of that theory where a noncommittal model ts one m which as many thmgs are possible as possible nonmonotomc 4 is probably the most interesting of the three since it is stronger than ordinary 4 but has all the usual inferential machinery of 4 there is a straightforward proof procedure for the sententlal subset of nonmonotomc 4 this approach to nonmonotonlc logic may be applied to several problems in knowledge representation for aruficml mtelhgence its main advantages over competmg approaches are that tt factors out problems of resource hmltattons and allows the symbol m to appear m any context since m is a meaningful part of the language

order statistic properties random generation and goodness of fit testing for a minimal repair model abstract we present properties of statistics arising from the block borges and savits age dependent minimal repair model these properties are analogous to the order statistic properties in homogeneous poisson processes these properties are exploited to obtain an algorithm for generating a realization from the minimal repair model and for testing hypothesis concerning the initial distribution function or hazard function of the repair model

a comparison of frailty models for multivariate survival data this paper reviews some of the main approaches to the analysis of multivariate censored survival data such data typically have correlated failure times the correlation can be a consequence of the observational design for example with clustered sampling and matching or it can be a focus of interest as in genetic studies longitudinal studies of recurrent events and other studies involving multiple measurements we assume that the correlation between the failure or survival times can be accounted for by fixed or random frailty effects we then compare the performance of conditional and mixture likelihood approaches to estimating models with these frailty effects in censored bivariate survival data we find that the mixture methods are surprisingly robust to misspecification of the frailty distribution the paper also contains an illustrative example on the times to onset of chest pain brought on by three endurance exercise tests during a drug treatment trial of heart patients

the marshall olkin alpha power family of distributions with applications abstract in this paper we introduce the marshall olkin alpha power family of distributions to extend the alpha power transform class defined by mahdavi and kundu 2017 and several other distributions the new family is analytically tractable and it can be used quite effectively for real data analysis some of its structural properties are established members of the new family can have symmetrical right skewed and reversed j shaped densities and increasing decreasing upside down bathtub and reversed j shaped hazard rates the model parameters are obtained by the method of maximum likelihood estimation we illustrate the performance of the proposed new family of distributions by means of three real data sets and the data sets show the new family of distributions is more appropriate as compared to the marshall olkin generalized lindley marshall olkin generalized exponential marshall olkin logistic exponential marshall olkin exponential exponentiated exponential transmuted generalized exponential alpha power exponential and exponential distributions

the accelerated gap times model summary this paper develops a new semiparametric model for the effect of covariates on the conditional intensity of a recurrent event counting process the model is a transparent extension of the accelerated failure time model for univariate survival data estimation of the regression parameter is motivated by semiparametric efficiency considerations extending the class of weighted log rank estimating functions originally proposed in prentice 1978 and subsequently studied in detail by tsiatis 1990 and ritov 1990 a novel rank based one step estimator for the regression parameter is proposed an aalen type estimator for the baseline intensity function is obtained asymptotics are handled with empirical process methods and finite sample properties are studied via simulation finally the new model is applied to the bladder tumour data of byar 1980

new classes of power series bivariate copulas abstract zhang et al 2016 introduced a copula based on the geometric distribution here we introduce general classes of copulas containing zhang et al 2016 s copula as a particular case physical motivations are given for the general classes one of the general classes is shown to be more flexible by reanalyzing the two real data sets in zhang et al 2016

design of clinical trials for recurrent events with periodic monitoring this paper presents a design for randomized clinical trials in which incomplete data are collected on the occurrence of potentially recurrent events through periodic monitoring in particular events are assumed to arise according to a point process but information is available at the times of monitoring only if one or more events has occurred since the preceding monitoring point the event process is modelled via a piecewise poisson process and a proportional rates model is introduced to represent the difference in event rates between treatment groups the design was developed on the basis of a wald type test derived from the generalized estimating equations of liang and zeger biometrika 73 13 22 1986 robustification of the variance of the estimator of the treatment effect was considered under a random effects model with a semi parametric mixture distribution the design was adopted to address issues which arose in an osteoporosis trial conducted in japan

a theoretical characterization of nonlinear distortion effects in ofdm systems this paper presents a theoretical characterization of nonlinear distortion effects in orthogonal frequency division multiplexing ofdm transmission systems in the theoretical framework developed it is shown that the effects on the decision variables of the in band distortion introduced by a bandpass memoryless nonlinearity can be described by means of a complex gain and an additive gaussian term with zero mean and suitable variance analytical expressions for gain and variance are given the conditions which allow this description are emphasized and discussed as a consequence a completely analytical procedure to evaluate error probability is also obtained and illustrated using ofdm discrete multitone modulation dmt systems with rectangular pulse shaping for the soft envelope limiter nonlinearity a closed form is derived a comparison with simulation results is carried out to verify the accuracy of this method

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

a family of bivariate distributions generated by the bivariate bernoulli distribution abstract if x 1 x 2 is a sequence of independent bernoulli random variables the number of successes in the first n trials has a binomial distribution and the number of failures before the rth success has a negative binomial distribution from both the binomial and the negative binomial distributions the poisson distribution is obtainable as a limit moreover gamma distributions integer shape parameters are limits of negative binomial distributions and the normal distribution is a limit of negative binomial poisson and gamma distributions these basic facts from elementary probability have natural extensions to two dimensions because there is a unique natural bivariate bernoulli distribution in this article such extensions yielding a family of bivariate distributions are obtained and studied

nonmonotonic reasoning preferential models and cumulative logics abstract many systems that exhibit nonmonotonic behavior have been described and studied already in the literature the general notion of nonmonotonic reasoning though has almost always been described only negatively by the property it does not enjoy i e monotonicity we study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties we concentrate on a number of families of nonmonotonic consequence relations defined in the style of gentzen 13 both proof theoretic and semantic points of view are developed in parallel the former point of view was pioneered by gabbay 10 while the latter has been advocated by shoham 38 five such families are defined and characterized by representation theorems relating the two points of view one of the families of interest that of preferential relations turns out to have been studied by adams 2 the preferential models proposed here are a much stronger tool than adams probabilistic semantics the basic language used in this paper is that of propositional logic the extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper

families of multivariate distributions abstract for many years there has been an interest in families of bivariate distributions with marginals as parameters genest and mackay 1986a b showed that several such families that appear in the literature can be derived by a unified method a similar conclusion is obtained in this article through the use of mixture models these models might be regarded as multivariate proportional hazards models with random constants of proportionality the mixture models are useful for two purposes first they make some properties of the derived distributions more transparent the positive dependency property of association is sometimes exposed and a method for simulation of data from the distributions is suggested but the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters and they indicate obvious multivariate extensions some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter

uncertainty modeling by bilattice based squares and triangles in this paper ginsberg s fitting s theory of bilattices and in particular the associated constructs of bilattice based squares and triangles is introduced as an attractive framework for the representation of uncertain and potentially conflicting information paralleling goguen s l fuzzy set theory we recall some of the advantages of bilattice based frameworks for handling fuzzy sets and systems provide the related structures with adequately defined graded versions of the basic logical connectives and study their properties and relationships

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

nonparametric estimation of the bivariate survival function with an application to vertically transmitted aids summary in this paper we propose a nonparametric estimator of the bivariate survival function when the two durations are subject to right censoring we consider the situation where the duration variables are successive and are always observed in a particular order and the censoring mechanism bears on their sum rather than on each separately thus if they are correlated the second duration is right censored by a dependent variable a nonparametric maximum likelihood estimator is derived that takes the dependent censoring into account we also derive the asymptotic variance of the estimator and show how it can be estimated the methods are applied on a vertically acquired mother to child transmission aids data set the first duration corresponds to the hiv incubation period and the second to the period of aids

what does a conditional knowledge base entail abstract this paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation a conditional knowledge base consisting of a set of conditional assertions of the type if then represents the explicit defeasible knowledge an agent has about the way the world generally behaves we look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base in a previous paper kraus and the authors defined and studied preferential consequence relations they noticed that not all preferential relations could be considered as reasonable inference procedures this paper studies a more restricted class of consequence relations rational relations it is argued that any reasonable nonmonotonic inference procedure should define a rational relation it is shown that the rational relations are exactly those that may be represented by a ranked preferential model or by a nonstandard probabilistic model the rational closure of a conditional knowledge base is defined and shown to provide an attractive answer to the question of the title global properties of this closure operation are proved it is a cumulative operation it is also computationally tractable this paper assumes the underlying language is propositional

analysing inconsistent first order knowledgebases it is well known that knowledgebases may contain inconsistencies we provide a framework of measures based on a first order four valued logic to quantify the inconsistency of a knowledgebase this allows for the comparison of the inconsistency of diverse knowledgebases that have been represented as sets of first order logic formulae we motivate the approach by considering some examples of knowledgebases for representing and reasoning with ontological knowledge and with temporal knowledge analysing ontological knowledge including the statements about which concepts are subconcepts of other concepts and which concepts are disjoint can be problematical when there is a lack of knowledge about the instances that may populate the concepts and analysing temporal knowledge such as temporal integrity constraints can be problematical when considering infinite linear time lines isomorphic to the natural numbers or the real numbers or more complex structures such as branching time lines we address these difficulties by providing algebraic measures of inconsistency in first order knowledgebases

stochastic comparisons of series and parallel systems with dependent heterogeneous extended exponential components under archimedean copula abstract in this paper we discuss the usual stochastic star and convex transform orders of both series and parallel systems comprising heterogeneous and dependent extended exponential components under archimedean copula sufficient conditions are established for the star ordering between the lifetimes of series and parallel systems consisting of such dependent components under certain conditions on the archimedean copula and the parameters we also discuss convex transform order between the series and parallel systems these results generalize some existing results in the literature to the case of dependent components as well as to a general family of component lifetime distributions

a distributional model for repeated failure time measurements summary a standard model for repeated measurements is based on the multivariate normal distribution with equicorrelated variables a corresponding analysis is developed for weibull failure times the resulting distribution has some attractive properties for practical application to multivariate failure times

analysis of dependent survival data applied to lifetimes of amalgam fillings when studying lifetimes of amalgam fillings one is faced with the fact that each patient may contribute multiple survival data this creates a dependence problem and some methods for solving it are presented here analysis for individual patients with simple approaches for combining data is discussed first then a parametric frailty model is applied to analyse variation within and between patients the results are presented in the form of an empirical bayes estimate for each patient

a calculus for four valued sequential logic we present a complete axiomatisation for four valued sequential logic it consists of nine axioms from which all valid laws can be derived by equational reasoning these nine axioms are independent of each other

autoepistemic logic autoepistemic logic is one of the principal modes of nonmonotonic reasoning it unifies several other modes of nonmonotonic reasoning and has important application in logic programming in the paper a theory of autoepistemic logic is developed this paper starts with a brief survey of some of the previously known results then the nature of nonmonotonicity is studied by investigating how membership of autoepistemic statements in autoepistemic theories depends on the underlying objective theory a notion similar to set theoretic forcing is introduced expansions of autoepistemic theories are also investigated expansions serve as sets of consequences of an autoepistemic theory and they can also be used to define semantics for logic programs with negation theories that have expansions are characterized and a normal form that allows the description of all expansions of a theory is introduced our results imply algorithms to determine whether a theory has a unique expansion sufficient conditions stratification that imply existence of a unique expansion are discussed the definition of stratified theories is extended and under some additional assumptions efficient algorithms for testing whether a theory is stratified are proposed the theorem characterizing expansions is applied to two classes of theories k1 theories and ae programs in each case simple hypergraph characterization of expansions of theories from each of these classes is given finally connections with stable model semantics for logic programs with negation is discussed in particular it is proven that the problem of existence of stable models is np complete authors abstract

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

a review of some extensions to generalized linear models although generalized linear models are reasonably well known they are not as widely used in medical statistics as might be appropriate with the exception of logistic log linear and some survival models at the same time the generalized linear modelling methodology is decidedly outdated in that more powerful methods involving wider classes of distributions non linear regression censoring and dependence among responses are required limitations of the generalized linear modelling approach include the need for the iterated weighted least squares iwls procedure for estimation and deviances for inferences these restrict the class of models that can be used and do not allow direct comparisons among models from different distributions powerful non linear optimization routines are now available and comparisons can more fruitfully be made using the complete likelihood function the link function is an artefact necessary for iwls to function with linear models but that disappears once the class is extended to truly non linear models restricting comparisons of responses under different treatments to differences in means can be extremely misleading if the shape of the distribution is changing this may involve changes in dispersion or of other shape related parameters such as the skewness in a stable distribution with the treatments or covariates any exact likelihood function defined as the probability of the observed data takes into account the fact that all observable data are interval censored thus directly encompassing the various types of censoring possible with duration type data in most situations this can now be as easily used as the traditional approximate likelihood based on densities finally methods are required for incorporating dependencies among responses in models including conditioning on previous history and on random effects one important procedure for constructing such likelihoods is based on kalman filtering

on the peak to average power of ofdm signals based on oversampling orthogonal frequency division multiplexing ofdm introduces large amplitude variations in time which can result in significant signal distortion in the presence of nonlinear amplifiers we introduce a new bound for the peak of the continuous envelope of an ofdm signal based on the maximum of its corresponding oversampled sequence it is shown to be very tight as the oversampling rate increases the bound is then used to derive a closed form probability upper bound for the complementary cumulative distribution function of the peak to mean envelope power ratio of uncoded ofdm signals for sufficiently large numbers of subcarriers as another application of the bound for oversampled sequences we propose tight relative error bounds for computation of the peak power using two main methods the oversampled inverse fast fourier transform and the method introduced for coded systems based on minimum distance decoding of the code

any world assumptions in logic programming due to the usual incompleteness of information representation any approach to assign a semantics to logic programs has to rely on a default assumption on the missing information the stable model semantics that has become the dominating approach to give semantics to logic programs relies on the closed world assumption cwa which asserts that by default the truth of an atom is false there is a second well known assumption called open world assumption owa which asserts that the truth of the atoms is supposed to be unknown by default however the cwa the owa and the combination of them are extremal though important assumptions over a large variety of possible assumptions on the truth of the atoms whenever the truth is taken from an arbitrary truth space the topic of this paper is to allow any assignment i e interpretation over a truth space to be a default assumption our main result is that our extension is conservative in the sense that under the everywhere false default assumption cwa the usual stable model semantics is captured due to the generality and the purely algebraic nature of our approach it abstracts from the particular formalism of choice and the results may be applied in other contexts as well

further results on the non parametric linear regression model in survival analysis this paper gives further developments of a non parametric linear regression model in survival analysis three subjects are studied first martingale residuals originally developed for the cox model are introduced for our linear model their theory is developed and they are shown to be useful for judging goodness of fit the second focus of the paper is on the use of bootstrap replications to judge which features of the cumulative regression plots are likely to reflect real phenomena and not merely random variation in particular this is applied to judging whether the effect of a covariate disappears over time a problem for which no formal test exists the third subject is density type or kernel estimation of the regression functions themselves this might give more direct information than the cumulative plots the approaches are illustrated by data from a clinical trial of carcinoma of the oropharynx and by survival times of grafts in renal patients

life table methods for heterogeneous populations distributions describing the heterogeneity taking account of heterogeneity between the individuals in population based mortality studies is important a systematic way of describing heterogeneity is by an unobserved quantity called frailty entering the hazard multiplicatively until now most studies have used a gamma distributed frailty which is mathematically convenient for example the distribution among survivors is also gamma this paper shows that several other distributions have equally simple properties the main example being the inverse gaussian distribution consequences of the different distributions are examined the inverse gaussian makes the population homogeneous with time whereas for the gamma the relative heterogeneity is constant

applications of circumscription to formalizing common sense knowledge we present a new and more symmetric version of the circumscription method of nonmonotonic reasoning first described in mccarthy 1980 and some applications to formalizing common sense knowledge the applications in this paper are mostly based on minimizing the abnormality of different aspects of various entities included are nonmonotonic treatments of is a hierarchies the unique names hypothesis and the frame problem the new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription a still more general formalism called prioritized circumscription is briefly explored

proof theory of nelson s paraconsistent logic a uniform perspective the aim of this paper is to obtain a theoretical foundation of inconsistency tolerant or paraconsistent reasoning by presenting a comprehensive study of the structural proof theory of david nelson s paraconsistent logic inconsistency handling has a growing importance in computer science since inconsistencies may frequently occur in knowledge based and intelligent information systems paraconsistent inconsistency tolerant logics have been studied to cope with such inconsistencies in this paper proof systems for nelson s paraconsistent logic n4 are comprehensively studied the logic n4 is a fundamental system and known to be a common basis for various extended and useful paraconsistent logics some basic theorems including cut elimination normalization and completeness are uniformly proved using various embedding theorems a variety of sequent calculi and natural deduction systems for n4 and some closely related systems are presented and compared

multi valued logic programming semantics an algebraic approach abstract in this paper we introduce the notion of join irreducibility in the context of bilattices and present a procedural semantics for bilattice based logic programs which uses as its basis the join irreducible elements of the knowledge part of the bilattice the join irreducible elements in a bilattice represent the primitive bits of information present within the system in bilattices which have the descending chain property in their knowledge ordering these elements provide a small representative set completely characterizing the bilattice the overall complexity of the inference systems based on such bilattices can thus be reduced by restricting attention to the join irreducible elements

parametrized semantics of logic programs a unifying framework the different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms that are rule heads and whose logical values cannot be inferred from the rules for example the well founded semantics corresponds to the assumption that every such atom is false while the kripke kleene semantics corresponds to the assumption that every such atom is unknown in this paper we propose to unify and extend this assumption based approach by introducing parameterized semantics for logic programs the parameter holds the value that one assumes for all rule heads whose logical values cannot be inferred from the rules we work within multi valued logic with bilattice structure and we consider the class of logic programs defined by fitting following fitting s approach we define an operator that allows us to compute the parameterized semantic and to compare and combine semantics obtained for different values of the parameter we show that our approach captures and extends the usual semantics of conventional logic programs thereby unifying their computation

a new extension of weibull distribution properties and different methods of estimation abstract the weibull distribution has been generalized by many authors in recent years here we introduce a new generalization of the weibull distribution called alpha logarithmic transformed weibull distribution that provides better fits than some of its known generalizations the proposed distribution contains weibull exponential logarithmic transformed exponential and logarithmic transformed weibull distributions as special cases our main focus is the estimation from frequentist point of view of the unknown parameters along with some mathematical properties of the new model the proposed distribution accommodates monotonically increasing decreasing bathtub and unimodal and then bathtub shape hazard rates so it turns out to be quite flexible for analyzing non negative real life data we briefly describe different frequentist approaches namely maximum likelihood estimators percentile based estimators least squares estimators weighted least squares estimators maximum product of spacings estimators and compare them using extensive numerical simulations monte carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples the potentiality of the distribution is analyzed by means of two real data sets

a non gaussian state space model and application to prediction of records on developpe une classe de modeles qui generalisent le travail de smith 1979 et bathes 1975 pour des donnees censurees

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

testing for monotone trend in recurrent event processes tests for the presence of monotone trends in recurrent event processes have been proposed and studied by many authors however a general concept of trend is elusive and the dependence of the behavior of tests on the assumed definitions of no trend and trend and on the observation periods for the processes has been largely ignored we discuss these issues and study them through analytical results and simulation studies the article also presents robust tests for trend across multiple processes extends them to deal with interval censored event times and compares them and other well known trend tests with respect to the issues mentioned

mean residual life and inactivity time of a coherent system subjected to marshall olkin type shocks we consider coherent systems subjected to marshall olkin type shocks coming at random times and destroying components of the system the paper combines two important models coherent systems and marshall olkin type shocks and studies the mean residual life mrl and the mean inactivity time mit functions of coherent systems that is subjected to random shocks the considered models and theoretical results are supported with examples and graphical representations

an analysis for menstrual data with time varying covariates this paper concerns the analysis of menstrual data in particular methodology to identify variables that contribute to the variability of menstrual cycles both within and between women the basis for the proposed methodology is a parameterization of the mean length of a menstrual cycle conditional upon the past cycles and covariates this approach accommodates the length bias and censoring commonly found in menstrual data data from a longitudinal study of menstrual patterns and other variables among lese women of the ituri forest zaire illustrate the methodology a small simulation illustrates the bias caused by incorrectly deleting the censored cycles

a dynamic frailty model for multivariate survival data summary we consider the statistical modeling of data consisting of many study subjects with serially correlated multivariate survival responses the ordinary frailty model handles the serial correlation in such data by introducing an unobserved multiplicative random effect term called the frailty in the hazard function the frailties are often assumed to be identical for the survival times from the same unit we have generalized the frailty model by allowing the frailties to vary stochastically with the indices we have proposed a simple scheme to update the dynamic frailties this approach assumes that the random effects are gamma distributed at each occurrence the two gamma parameters are updated according to the past information in terms of their marginal distributions the dynamic frailties form a multiplicative random walk this approach results in a tractable likelihood the small sample behavior of the mle is studied via a simulation experiment the model is then illustrated with a data set from an animal carcinogenesis experiment

nonparametric estimation of a recurrent survival function abstract recurrent event data are frequently encountered in studies with longitudinal designs let the recurrence time be the time between two successive recurrent events recurrence times can be treated as a type of correlated survival data in statistical analysis in general because of the ordinal nature of recurrence times statistical methods that are appropriate for standard correlated survival data in marginal models may not be applicable to recurrence time data specifically for estimating the marginal survival function the kaplan meier estimator derived from the pooled recurrence times serves as a consistent estimator for standard correlated survival data but not for recurrence time data in this article we consider the problem of how to estimate the marginal survival function in nonparametric models a class of nonparametric estimators is introduced the appropriateness of the estimators is confirmed by statistical theory and simulations simulation and analysis from schizophrenia data are pre

disjunctive stable models disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning this paper focuses on stable model semantics currently the most widely acknowledged semantics for disjunctive logic programs after presenting a new notion of unfounded sets for disjunctive logic programs we provide two declarative characterizations of stable models in terms of unfounded sets one shows that the set of stable models coincides with the family of unfounded free models i e a model is stable iff it contains no unfounded atoms the other proves that stable models can be defined equivalently by a property of their false literals as a model is stable iff the set of its false literals coincides with its greatest unfounded set we then generalize the well founded wpoperator to disjunctive logic programs give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of function free programs the algorithm s soundness and completeness are proved and some complexity issues are discussed