ergodic properties of levy flights coexisting with subdiffusion and related models abstract we analyze ergodic properties of two different stationary processes resulting from a combination of levy flights and subdiffusion the first one comes from the lamperti transformation of subordinated stable process the second one is a sequence of increments of subordinated levy process we prove that both processes are mixing and ergodic we also study increments and the lamperti transformation of time changed fractional brownian motion it appears that these models of anomalous diffusion are also ergodic and mixing we believe that the derived results will help to verify ergodicity in single particle tracking experiments

inverse gaussian and its inverse process as the subordinators of fractional brownian motion in this paper we study the fractional brownian motion fbm time changed by the inverse gaussian ig process and its inverse called the inverse to the inverse gaussian iig process some properties of the time changed processes are similar to those of the classical fbm such as long range dependence however one can also observe different characteristics that are not satisfied by the fbm we study the distributional properties of both subordinators namely ig and iig processes and also that of the fbm time changed by these subordinators we establish also the connections between the subordinated processes considered and the continuous time random walk model for the application part we introduce the simulation procedures for both processes and discuss the estimation schemes for their parameters the effectiveness of these methods is checked for simulated trajectories

information theory and maximum product of spacings estimation summary a principle of least information is proposed for estimating continuous univariate distribu tions data are represented by quantiles the principle yields a reference distribution that is identical with the maximum product of spacings estimate a method to estimate continuous univariate distributions is proposed it is suitable when the distribution type is uncertain or when the data are only a small random sample in 1957 jaynes presented the maximum entropy approach to estimation jaynes 1983 which is valid for discrete random variables the product is the least biased estimate possible for the information given data in jaynes s analysis are in the form of a finite set of moments the analysis was extended to continuous random variables by kullback and leibler and axiomatized by shore and johnson 1980 it uses moments and requires an unspecified prior distribution a development of jaynes s entropy theory is presented here the analysis is derived from the kullback leibler relative entropy but uses quantiles instead of moments and gives a minimum information principle for selecting the prior i e the reference distribution p in the univariate case p is identical with the maximum product of spacings mps distribution due to cheng and amin 1983 and ranneby 1984 the mps method thus finds a rationale in information theory conversely these and more recent works titterington 1985 cheng and stephens 1989 provide information on some of the properties of the method proposed in general the mps distribution p does not satisfy the constraints of the sample rule stated here it is not a minimum information model but an approximation there is however a unique model called the posterior q that is closest to p in that it minimizes the relative entropy with respect to p and satisfies the constraints of the data the two minimum principles for p and q are unified into a principle of least information for selection of the reference distribution and determination of the posterior distribution cheng and amin 1983 considered a candidate set in the form of distributions with density p x 6 and cumulative density function p x 6 where 6 is a parameter vector they mapped the sample x and the end points of the domain of x into the unit interval 0 1 by using the transformation y p x 6 subdividing the unit interval into m spacings their mps method chooses 6 to maximize the geometric

fractional levy stable motion can model subdiffusive dynamics we show in this paper that the sample time average mean squared displacement msd of the fractional levy stable motion behaves very differently from the corresponding ensemble average second moment while the ensemble average msd diverges for 2 the sample msd may exhibit either subdiffusion normal diffusion or superdiffusion thus h self similar levy stable processes can model either a subdiffusive diffusive or superdiffusive dynamics in the sense of sample msd we show that the character of the process is controlled by a sign of the memory parameter d h 1 we also introduce a sample p variation dynamics test which allows to distinguish between two models of subdiffusive dynamics finally we illustrate a subdiffusive behavior of the fractional levy stable motion on biological data describing the motion of individual fluorescently labeled mrna molecules inside live e coli cells but it may concern many other fields of contemporary experimental physics doi 10 1103 physreve 82 021130

the existence of positive solutions and oscillation of solutions of higher order difference equations with forcing terms sufficient conditions are established for the existence of positive solutions and oscilla tion of all bounded solutions of the neutral difference equation ap zn can l t qnf zn k hn n no where a is the forward difference operator azn xn l xn i and k are integers c i is a real number and qn and hn are real sequences it is also shown that some of these sufficient conditions are necemary 1998 elsevier science ltd all rights reserved

reliability estimation of stress strength model using finite mixture distributions under progressively interval censoring abstract this paper considers the reliability estimation of the stress strength model based on progressively type i interval censored data where the random stress variable follows a lindley distribution and the random strength variable follows a finite mixture of exponential distributions the maximum likelihood estimation and 95 confidence interval estimation of the stress strength reliability are deduced by using em algorithm and bootstrap sampling respectively the bayesian estimation and 95 highest posterior density credible interval of the stress strength reliability under squared error loss function are obtained by using the metropolis hastings within gibbs algorithm to test the homogeneity of the finite mixture distributions the d test statistic is introduced then we use the d test statistic to test the homogeneity of a real data compare the finite mixture exponential distributions with a single exponential distribution by using the akaike information criterion aic values and analyze this data using the proposed methodology finally monte carlo simulations are performed for illustrative purpose

non regular maximum likelihood problems four non regular estimation problems are reviewed and discussed one the unbounded likelihood problem involves distributions with infinite spikes for which maximum likelihood can fail to give consistent estimators a comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case an application to the box cox shifted power transform is given the other three problems occur when the true parameter lies in some special subregion in one the constrained parameter problem the subregion is a boundary the other two the embedded model and the indeterminate parameters problems occur when the model takes on a special form in the subregion these last two problems have previously been investigated separately we show that they are equivalent in some situations both often arise in non linear models and we give a directed graph approach which allows for their occurrence in nested model building it is argued that many non regular problems can be handled systematically without having to resort to elaborate technical assumptions relatively uncomplicated methods may be used provided that the underlying nature of the non regularity is understood

stress strength reliability analysis of system with multiple types of components using survival signature abstract in this paper we study the estimation for stress strength reliability of the system with multiple types of components based on survival signature in the situation that different types of components are subjected to different types of random stresses the maximum likelihood estimator maximum spacing estimator bootstrap p confidence interval two point estimators and generalized confidence interval using generalized pivotal quantity for system stress strength reliability are derived under the assumption that the stresses and strengths variables follow the gompertz distributions with common or unequal scale parameters additionally when the stresses and strengths variables follow the gompertz distributions with unequal scale parameters a modified generalized confidence interval for the system stress strength reliability based on the fisher z transformation is also proposed in the situation that the system is subjected to the common stress the above point estimators and confidence intervals for the system stress strength reliability are also developed monte carlo simulations are performed to compare the performance of these point estimators and confidence intervals a real data analysis is presented for an illustration of the findings

statistical inference of weibull distribution based on generalized progressively hybrid censored data abstract weibull distribution and generalized progressive hybrid censoring scheme gphcs have been used widely in reliability engineering the gphcs can improve the efficiency of statistical inference by allowing experimenters to observe a pre assigned number of failure samples within a proper testing period in this paper we consider maximum likelihood least squares ls weighted least squares wls and maximum product of spacings mps estimates for two parameter weibull distribution under the assumption that samples are generalized progressively hybrid censored the maximum likelihood estimation mle of unknown parameter is obtained using newton raphson algorithm and expectation maximization em algorithm the asymptotic normality of the mle and bootstrap method are used to construct approximate confidence intervals a parametric bootstrap goodness of fit gof testing is proposed for the weibull distribution with generalized progressively hybrid censored sample extensive monte carlo simulations are conducted to assess the proposed methods finally one real data set is analyzed for illustrative purposes

fractional brownian motion and motion governed by the fractional langevin equation in confined geometries motivated by subdiffusive motion of biomolecules observed in living cells we study the stochastic properties of a non brownian particle whose motion is governed by either fractional brownian motion or the fractional langevin equation and restricted to a finite domain we investigate by analytic calculations and simulations how time averaged observables e g the time averaged mean squared displacement and displacement correlation are affected by spatial confinement and dimensionality in particular we study the degree of weak ergodicity breaking and scatter between different single trajectories for this confined motion in the subdiffusive domain the general trend is that deviations from ergodicity are decreased with decreasing size of the movement volume and with increasing dimensionality we define the displacement correlation function and find that this quantity shows distinct features for fractional brownian motion fractional langevin equation and continuous time subdiffusion such that it appears an efficient measure to distinguish these different processes based on single particle trajectory data

computing optimal confidence sets for pareto models under progressive censoring this paper presents two families of joint confidence sets for the pareto shape and precision parameters based on progressively censored data which include the existing regions in the literature as particular cases and derives explicit expressions for the corresponding areas upon using fiducial arguments an exact and quick computational method is then proposed in order to find the smallest area pareto region which depends on the minimal sufficient statistic with a specified confidence level shortest length confidence intervals for the pareto parameters are also provided the reduction in area of the minimal joint confidence region with respect to the existing sets is substantial in most situations and impressive in some cases for illustrative and comparative purposes two practical studies concerning device lifetimes and business failures are considered applications of the smallest confidence sets include uses in hypothesis testing and estimation in particular it is possible to construct confidence intervals for functions of the pareto parameters as well as pointwise and simultaneous confidence bands for the pareto reliability function

expected total test time and bayesian estimation for generalized lindley distribution under progressively type ii censored sample where removals follow the beta binomial probability law in this paper we have proposed the progressive type ii censoring scheme which allows the removals of the live units from a life test with beta binomial probability law during the execution of the experiment to stablish the theory the generalized lindley distribution is considered for our proposed procedure the behaviour of the expected total test time has been investigated through the numerical study the classical as well as the bayesian procedures for the estimation of the unknown model parameters have also been developed under this censoring scheme further the discussion has been extended to the prediction of the future samples under bayesian paradigm finally a real data set has been analysed to illustrate the discussed methodology

stress strength reliability analysis of multi state system based on generalized survival signature abstract the stress strength model has been widely used in reliability design of system in the traditional stress strength reliability theory the system and each component are assumed to be only in one of two possible states being either working or failed and the notion of stress strength reliability is the probability that the strength is larger than the stress in this paper we study the stress strength reliability of multi state system based on generalized survival signature it is supposed that the state of multi state system is defined by using the ratio between strength and stress random variables the definitions of generalized survival signature for a certain class of multi state systems with multi state components in both discrete and continuous cases are given in addition the expressions of stress strength reliability in both discrete and continuous situations are derived in the case of continuous multi state system it is assumed that the random strength and stress are both from the weibull distributions with different scale parameters and the two different continuous kernel functions are pareto and generalized half logistic distribution functions respectively based on the assumptions the stress strength reliability is estimated by using both classical and bayesian statistical theories the uniformly minimum variance unbiased estimator and maximum likelihood estimator for the stress strength reliability of the continuous multi state system are derived under the squared error loss function the exact expression of bayes estimator for the stress strength reliability of the continuous multi state system is developed by using gauss hypergeometric function finally the monte carlo simulations are performed to compare the performances of the proposed stress strength reliability estimators and a real data set is also analyzed for an illustration of the findings

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

forecasting records by maximum likelihood abstract a maximum likelihood method of fitting a model to a series of records is proposed using ideas from the analysis of censored data to construct a likelihood function based on observed records this method is tried out by fitting several models to series of athletics records for mile and marathon races a form of residual analysis is proposed for testing the models forecasting consequences are also considered in the case of mile records a steady linear improvement since 1931 is found the marathon data are harder to interpret with a steady improvement until 1965 with only slight improvement in world records since then in both cases the normal distribution appears at least as good as extreme value distributions for the distribution of annual best performances short term forecasts appear satisfactory but serious reservations are expressed about using regression type methods to predict long term performance limits

computer assisted analysis of mixtures c a man statistical algorithms summary this paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one parameter family of densities and provides a unifying computeroriented concept for the statistical analysis of unobserved heterogeneity i e observations stemming from different subpopulations in a univariate sample the case with unknown number of population subgroups as well as the case with known number of population subgroups with emphasis on the first is considered in the computer package c a man computer assisted mixture analysis it includes an algorithmic menu with choices of the em algorithm the vertex exchange algorithm a combination of both as well as the vertex direction method to ensure reliable convergence a steplength menu is provided for the three latter methods each achieving monotonicity for the direction of choice c a man has the option to work with restricted support size that is the case when the number of components is known a priori in the latter case the em algorithm is used applications of mixture modelling in medical problems are discussed

geometric brownian motion with tempered stable waiting times one of the earliest system that was used to asset prices description is black scholes model it is based on geometric brownian motion and was used as a tool for pricing various financial instruments however when it comes to data description geometric brownian motion is not capable to capture many properties of present financial markets one can name here for instance periods of constant values therefore we propose an alternative approach based on subordinated tempered stable geometric brownian motion which is a combination of the popular geometric brownian motion and inverse tempered stable subordinator in this paper we introduce the mentioned process and present its main properties we propose also the estimation procedure and calibrate the analyzed system to real data

stress strength reliability in the presence of fuzziness this paper investigates the stress strength reliability in the presence of fuzziness the fuzzy membership function is defined as a function of the difference between stress and strength values and the fuzzy reliability of single unit and multicomponent systems are calculated the inclusion of fuzziness in the stress strength interference enables the user to make more sensitive analysis illustrations are presented for various stress and strength distributions

geometry of exponential family with competing risks and censored data abstract employing the differential geometrical methods in statistics suggested by amari 1985 and amari et al 1987 considering the exponential family with censored data and competing risks as a manifold of a statistical model the geometry of the manifold is investigated based on two information sources as an application of the geometry the asymptotic expansions of the bootstrap prediction bayesian prediction and their risk evaluations are investigated the results show that these expansions are related to the coefficients of connections and metric tensors and the predictive density function is the estimative density function in the asymptotic sense finally taking rayleigh distribution and prostatic cancer data as examples some computation and simulation results are presented to illustrate our main results

estimation of nonlinear functionals of densities with confidence this paper introduces a class of k nearest neighbor k nn estimators called bipartite plug in bpi estimators for estimating integrals of nonlinear functions of a probability density such as shannon entropy and renyi entropy the density is assumed to be smooth have bounded support and be uniformly bounded from below on this set unlike previous k nn estimators of nonlinear density functionals the proposed estimator uses data splitting and boundary correction to achieve lower mean square error specifically we assume that t i i d samples xi rd from the density are split into two pieces of cardinality m and n respectively with m samples used for computing a k nn density estimate and the remaining n samples used for empirical estimation of the integral of the density functional by studying the statistical properties of k nn balls explicit rates for the bias and variance of the bpi estimator are derived in terms of the sample size the dimension of the samples and the underlying probability distribution based on these results it is possible to specify optimal choice of tuning parameters m t k for maximizing the rate of decrease of the mean square error the resultant optimized bpi estimator converges faster and achieves lower mean squared error than previous k nn entropy estimators in addition a central limit theorem is established for the bpi estimator that allows us to specify tight asymptotic confidence intervals

reliability of coherent systems with a single cold standby component in this paper the influence of a cold standby component on a coherent system is studied a method for computing the system reliability of coherent systems with a cold standby component based on signature is presented numerical examples are presented reliability and mean time to failure of different systems are computed

subdiffusion of mixed origins when ergodicity and nonergodicity coexist single particle trajectories are investigated assuming the coexistence of two subdiffusive processes diffusion on a fractal structure modeling spatial constraints on motion and heavy tailed continuous time random walks representing energetic or chemical traps the particles mean squared displacement is found to depend on the way the mean is taken temporal averaging over single particle trajectories differs from averaging over an ensemble of particles this is shown to stem from subordinating an ergodic anomalous process to a nonergodic one the result is easily generalized to the subordination of any other ergodic process i e fractional brownian motion to a nonergodic one for certain parameters the ergodic diffusion on the underlying fractal structure dominates the transport yet displaying ergodicity breaking and aging

oscillation theorems for neutral difference equations abstract oscillation criteria for first order difference equations of the form x n q n x n 0 and x n px n k q n x n f n are established here xn xn 1 xn is the forward difference operator 1 p is a real number and k are nonnegative integers qn fn are sequences of nonnegative real numbers and r r is continuous oscillation criteria for nonlinear difference equations of sublinear as well as superlinear type are also established

semiparametric estimation of normal mixture densities a semiparametric method for estimating densities of normal mean mixtures is presented this consistent data driven method of estimation is based on probability spacings the estimation technique involves iteratively fixing the standard deviation of the normal kernel that serves as a smoothing parameter and then maximizing a function of the probability spacings over all mixing distributions based on the distribution of uniform spacings a distribution free goodness of fit criterion is developed to guide the selection of the smoothing parameter the result is a set of consistent estimators indexed by a range of smoothing parameters empirical process results are used to prove consistency

importance of components in k out of n system with components having random weights the purpose of this paper is to study the component importance in k out of n system with components having random weights the system works if at least k components work and the total weight of all working components is above the required level c a new measure of component importance called weighted importance for such a system is introduced and its relation with birnbaum reliability measure of importance is studied it is shown that the larger weight stochastically implies the larger weighted measure of importance it is also shown that if two components are identically distributed then the larger weight stochastically implies the larger birnbaum reliability measure of importance finally it is proved that if the weight of a component is stochastically increased then the weighted and birnbaum reliability measures of importance are increased accordingly

a simulation based approach to the parameter estimation for the three parameter gamma distribution abstract the gamma distribution is one of the commonly used statistical distribution in reliability while maximum likelihood has traditionally been the main method for estimation of gamma parameters hirose has proposed a continuation method to parameter estimation for the three parameter gamma distribution in this paper we propose to apply markov chain monte carlo techniques to carry out a bayesian estimation procedure using hirose s simulated data as well as two real data sets the method is indeed flexible and inference for any quantity of interest is readily available

on flexible progressive censoring in life testing experiment under the setup of progressive type ii censoring we consider a new flexible scheme in which the experimenter removes r 1 r 1 r 1 units from the experiment if the first failure occurs before some predefined time t 1 and removes r 1 units when the first failure occurs after time t 1 if the second failure occurs before the time t 2 r 2 surviving items are removed at random otherwise r 2 surviving units are removed r 2 r 2 and so on finally after the mth failure all remaining items are removed under this setup of the experiment we study the distributions of failure times which are entitled as flexible progressive type ii censored fpc order statistics the simulation algorithm for generating fpc samples and an illustrative example for a special case of exponential distribution are also presented finally a monte carlo study is also conducted for the expected termination time under fcp

on the comparison of reliability experiments based on the convolution order in this article we study the comparison of experiments in system reliability theory when the component lifetimes are independent and identically distributed random variables that have a common two parameter exponential distribution with a location parameter for this purpose we define a new stochastic order which we call the convolution order and study some basic properties of it we then focus our attention on the family of distribution functions that are mixtures of distributions of partial sums of independent exponential random variables and derive results that identify several conditions under which members of this family are ordered in the convolution stochastic order we apply the results to order lifetimes of coherent systems and as a consequence we obtain information inequalities among various lifetimes of coherent systems we find situations wherein high reliability decreases statistical information

a new upside down bathtub shaped hazard rate model for survival data analysis abstract in medical engineering besides demography and other applied disciplines it is pronounced in some applications that the hazard rate of the data initially increased to a pick in the beginning age declined abruptly till it stabilized in statistics literature such hazard rate is known as the upside down bathtub shaped hazard rate and propound in the various survival studies in this paper we proposed a transmuted inverse rayleigh distribution which possesses the upside down bathtub shape for its hazard rate the fundamental properties such as mean variance mean deviation order statistics renyi entropy and stress strength reliability of the proposed model are explored here further three methods of estimation namely maximum likelihood least squares and maximum product spacings methods are used for estimating the unknown parameters of the transmuted inverse rayleigh distribution and compared through the simulation study finally the applicability of the proposed distribution is shown for a set of real data representing the times between failures of the secondary reactor pumps

on the oscillation of solutions and existence of positive solutions of neutral difference equations abstract we obtain sufficient conditions for the oscillation of all solutions and existence of positive solutions of the neutral difference equation x n cx n m p n x n k 0 n 0 1 2 where c and p n are real numbers m and k are integers and p n m and k are nonnegative

bayesian likelihood methods for estimating the end point of a distribution summary we consider maximum likelihood methods for estimating the end point of a distribution the likelihood function is modified by a prior distribution that is imposed on the location parameter the prior is explicit and meaningful and has a general form that adapts itself to different settings results on convergence rates and limiting distributions are given in particular it is shown that the limiting distribution is non normal in non regular cases parametric bootstrap techniques are suggested for quantifying the accuracy of the estimator we illustrate performance by applying the method to multiparameter weibull and gamma distributions

inference from grouped data in three parameter weibull models with applications to breakdown voltage experiments an important objective of breakdown voltage experiments is to estimate either the threshold below which no breakdown occurs or other voltage levels below which breakdown occurs with a small probability a commonly used statistical technique in these studies is to fit a three parameter weibull distribution to the experimental data difficulties in applying the method of maximum likelihood to three parameter weibull models due to nonregularity have led to a variety of alternative approaches in the literature in practice however voltage breakdown and other failure time data are usually discretized or rounded off for grouped data from the weibull model there are still difficulties in applying likelihood methods when the sample size is moderate because of the so called embedded model problem after a brief review of this problem and related likelihood theory we show how the difficulties can be resolved and how likelihood based confidence intervals for the weibull parameters and quantiles can be constru

asymptotic behavior of nonoscillatory solutions of neutral difference equations the authors consider the mth order neutral difference equation dm y n p n y n k q n f y n e n where m 1 p n q n e n and a1 n a2 n am 1 n are real sequences ai n 0 for i 1 2 m 1 am n 1 d0z n y n p n y n k diz n ai n di 1z n for i 1 2 m k is a positive integer n is a sequence of positive integers and r r is continuous with u f u 0 for u 0 in the case where q n is allowed to oscillate they obtain sufficient conditions for all bounded nonoscillatory solutions to converge to zero and if q n is a nonnegative sequence they establish sufficient conditions for all nonoscillatory solutions to converge to zero examples illustrating the results are included throughout the paper

ergodic properties of fractional brownian langevin motion we investigate the time average mean square displacement overline ensuremath delta 2 mathbf x t mathbf ensuremath int 0 t ensuremath ensuremath delta x t ensuremath ensuremath delta ensuremath x t ensuremath 2 d t ensuremath t ensuremath ensuremath delta for fractional brownian langevin motion where x t is the stochastic trajectory and ensuremath delta is the lag time unlike the previously investigated continuous time random walk model overline ensuremath delta 2 converges to the ensemble average x 2 ensuremath sim t 2h in the long measurement time limit the convergence to ergodic behavior is slow however and surprisingly the hurst exponent h frac 3 4 marks the critical point of the speed of convergence when hl frac 3 4 the ergodicity breaking parameter e b mathbf overline ensuremath delta 2 mathbf x t mathbf mathbf 2 ensuremath overline ensuremath delta 2 mathbf x t mathbf 2 mathbf overline ensuremath delta 2 mathbf x t mathbf 2 ensuremath sim k h ensuremath delta t ensuremath 1 when h frac 3 4 e b ensuremath sim frac 9 16 mathrm ln phantom rule 0 2em 0ex t ensuremath delta t ensuremath 1 and when frac 3 4 lhl1 e b ensuremath sim k h ensuremath delta 4 ensuremath 4h t 4h ensuremath 4 in the ballistic limit h ensuremath rightarrow 1 ergodicity is broken and e b ensuremath sim 2 the critical point h frac 3 4 is marked by the divergence of the coefficient k h fractional brownian motion as a model for recent experiments of subdiffusion of mrna in the cell is briefly discussed and a comparison with the continuous time random walk model is made

existence of maximum likelihood estimates for interval censored data from some three parameter models with a shifted origin summary given data in the form of interval censored observations from a three parameter distribution practical criteria are established for the existence of maximum likelihood estimates for three kinds of parameter space these criteria can be derived by analysing the behaviour of the log likelihood near a type of boundary of the parameter space called the probability contents inner boundary the effectiveness of the criteria is discussed in the case where the underlying distribution is a three parameter log normal distribution the efficiency of the criteria is evaluated by simulation

attribute and size reduction mechanisms in multi adjoint concept lattices attribute reduction and size reduction in concept lattices are key research topics in formal concept analysis fca this paper combines both strategies in the multi adjoint concept lattice framework in order to simplify the information provided by the original context specifically we present three procedures which merge the attribute reduction and the size reduction by means of an irreducible cut concept lattice analyzing the obtained properties

a goodness of fit test using moran s statistic with estimated parameters summary moran s log spacings statistic for testing goodness of fit is shown to have the same asymptotic distribution when parameters must be estimated from the sample as it does when parameters are known provided the estimation is done efficiently for small samples a chi squared approximation is given and shown to be accurate when estimation is carried out by minimizing moran s statistic itself regarded as a function of the unknown parameters a numerical example is given to show the usefulness of moran s statistic

embedded models in three parameter distributions and their estimation summary two distinct problems can arise in maximum likelihood estimation in certain threeparameter problems one problem associated with the fitting of a threshold parameter occurs if the fitted distribution has to be very positively skewed this problem is well known however there is a second and unrelated difficulty which occurs quite often in practice and which arises when the distribution is not at all skew this problem is not so well understood it is shown in this paper that within the three parameter model there is an embedded twoparameter special case which corresponds to infinite parameter values in the original model the problem arises when this embedded model is the best fit to the data the problem is shown to be easily resolved by first carrying out a check to see whether the embedded model should be fitted instead of the three parameter model formal tests for this are discussed the gamma inverse gaussian log normal and weibull distributions are examples where the problem occurs numerical examples are provided for illustration

subordinated α stable ornstein uhlenbeck process as a tool for financial data description abstract the classical financial models are based on the standard brownian diffusion type processes however in the exhibition of some real market data like interest or exchange rates we observe characteristic periods of constant values moreover in the case of financial data the assumption of normality is often unsatisfied in such cases the popular vasicek model that is a mathematical system describing the evolution of interest rates based on the ornstein uhlenbeck process seems not to be applicable therefore we propose an alternative approach based on a combination of the popular ornstein uhlenbeck process with a stable distribution and subdiffusion systems that demonstrate such characteristic behavior the probability density function of the proposed process can be described by a fokker planck type equation and therefore it can be examined as an extension of the basic ornstein uhlenbeck model in this paper we propose the parameters estimation method and calibrate the subordinated vasicek model to the interest rate data

a generalization of the beta distribution with applications abstract this paper introduces a five parameter beta distribution gb which nests the generalized beta and gamma distributions and includes more than thirty distributions as limiting or special cases the generalized beta leads to an exponential generalized beta egb distribution which includes generalized forms of the logistics exponential gompertz and gumbell distributions and the normal as special cases the egb family of distributiosn provides the basis for partially adaptive estimation of econometric models with possibly skewed and leptokurtic error distributions applications of the models to investigating the distribution of income stock returns and in regression analysis are considered

predicting monthly streamflow using data driven models coupled with data preprocessing techniques 1 in this paper the accuracy performance of monthly streamflow forecasts is discussed when using data driven modeling techniques on the streamflow series a crisp distributed support vectors regression cdsvr model was proposed for monthly streamflow prediction in comparison with four other models autoregressive moving average arma k nearest neighbors knn artificial neural networks anns and crisp distributed artificial neural networks cdann with respect to distributed models of cdsvr and cdann the fuzzy c means fcm clustering technique first split the flow data into three subsets low medium and high levels according to the magnitudes of the data and then three single svrs or anns were fitted to three subsets this paper gives a detailed analysis on reconstruction of dynamics that was used to identify the configuration of all models except for arma to improve the model performance the data preprocessing techniques of singular spectrum analysis ssa and or moving average ma were coupled with all five models some discussions were presented 1 on the number of neighbors in knn 2 on the configuration of ann and 3 on the investigation of effects of ma and ssa two streamflow series from different locations in china xiangjiaba and danjiangkou were applied for the analysis of forecasting forecasts were conducted at four different horizons 1 3 6 and 1 2 month ahead forecasts the results showed that models fed by preprocessed data performed better than models fed by original data and cdsvr outperformed other models except for at a 6 month ahead horizon for danjiangkou for the perspective of streamflow series the ssa exhibited better effects on danjingkou data because its raw discharge series was more complex than the discharge of xiangjiaba the ma considerably improved the performance of ann cdann and cdsvr by adjusting the correlation relationship between input components and output of models it was also found that the performance of cdsvr deteriorated with the increase of the forecast horizon

mle and the estimated expected test time for the two parameter gompertz distribution under progressive censoring with binomial removals this study considers the estimation of two parameter gompertz distribution under type ii progressive censoring with random removals where the number of units removed at each failure time follows a binomial or a uniform distribution the maximum likelihood estimates of two parameters and their asymptotic distribution are derived the expected termination point to complete the censoring test is computed and analyzed for different censoring schemes for binomial removals the effect of various p on the expected termination point under progressive censoring and the relative expected termination point over the complete sample reet1 are investigated in this article for random removals pcr the expected termination point is computed and the relative expected termination point over the complete sample reet2 are also investigated

a new image thresholding method based on gaussian mixture model in this paper an efficient approach to search for the global threshold of image using gaussian mixture model is proposed firstly a gray level histogram of an image is represented as a function of the frequencies of gray level then to fit the gaussian mixtures to the histogram of image the expectation maximization em algorithm is developed to estimate the number of gaussian mixture of such histograms and their corresponding parameterization finally the optimal threshold which is the average of these gaussian mixture means is chosen and the experimental results show that the new algorithm performs better

risk analysis under progressive type ii censoring with binomial claim numbers this paper presents a model of actuarial loss events that follow a progressive censoring scheme loss events are modelled according to this scheme regarding the claim number and size claim events at random time points are assumed to happen progressively in a given period due to each of an m number of claims that occur due to hazardous events while a fixed number of n claims are anticipated to take place in total distribution of the resulting total loss amount is derived and according to its properties some risk management issues about reserves and solvency are discussed

a bayesian analysis of record statistics from the gompertz model the gompertz distribution has been used as a growth model and it can be used to fit tumor growth record values can be viewed as order statistics from a sample whose size is determined by the values and the order of occurrence of observations based on record values from the two parameter gompertz distribution bayes estimators for the two unknown parameters are obtained by using laplace approximation these estimates are obtained based on the squared error and linex loss functions predictions for future upper record values from the gompertz model are obtained from a bayesian approach the maximum likelihood and bayes estimates are compared via monte carlo simulation study and a numerical example is given to illustrate the results of prediction

order statistics from mixed exchangeable random variables two different exchangeable samples are considered and these two samples are assumed to be independent of each other from these two samples a new sample is combined and treated as a single set of observations the distribution of a single order statistic and the joint distribution of two order statistics for a new mixed sample are derived and expressed in terms of joint distribution functions as a special case the distribution of a single order statistic and the joint distribution of two nonadjacent order statistics from exchangeable random variables are obtained the results presented in this paper allows widespread applications in modelling of various lifetime data biomedical sciences reliability and survival analysis actuarial sciences etc where the assumption of independence of data cannot be accepted and the exchangeability is a more realistic assumption

langevin picture of subdiffusion with infinitely divisible waiting times in this paper we study a langevin approach to modeling of subdiffusion in the presence of time dependent external forces we construct a subordinated langevin process whose probability density function solves the subdiffusive fractional fokker planck equation we generalize the results known for the levy stable waiting times to the case of infinitely divisible waiting time distributions our approach provides a complete mathematical description of subdiffusion with time dependent forces moreover it allows to study the trajectories of the constructed process both analytically and numerically via monte carlo methodology

on fractional tempered stable processes and their governing differential equations we derive the governing equation of the tempered stable subordinator hereafter tss which generalizes the space fractional differential equation satisfied by the law of the stable subordinator itself this equation is expressed in terms of the shifted fractional derivative of order 0 1 coinciding with the stability parameter we then generalize this equation by introducing a time fractional derivative of order 0 1 resp 1 1 and we prove that it is satisfied by the law of a tss time changed by the inverse of a stable subordinator resp by the stable subordinator itself the corresponding processes can therefore be called fractional ts processes finally we provide fractional extensions of the relativistic stable processes which we define as a brownian motion with a random time argument represented by independent fractional ts processes of order resp 1

reliability estimation of a n m cold standby redundancy system in a multicomponent stress strength model with generalized half logistic distribution abstract in this paper we study the estimation for the reliability of a multicomponent system named n m cold standby redundancy system based on progressive type ii censoring sample in the system there are n subsystems consisting of m statistically independent distributed strength components and only one of these subsystems works under the impact of stresses at a time and the others remain as standbys whenever the working subsystem fails one from the standbys takes its place the system fails when the entire subsystems fail it is supposed that the underlying distributions of random strength and stress both belong to the generalized half logistic distribution with different shape parameter the reliability of the system is estimated by using both classical and bayesian statistical inference uniformly minimum variance unbiased estimator and maximum likelihood estimator for the reliability of the system are derived under squared error loss function the exact expression of the bayes estimator for the reliability of the system is developed by using the gauss hypergeometric function the asymptotic confidence interval and corresponding coverage probabilities are derived based on both the fisher and the observed information matrices the approximate highest probability density credible interval is constructed by using monte carlo method monte carlo simulations are performed to compare the performances of the proposed reliability estimators a real data set is also analyzed for an illustration of the findings

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

weak ergodicity breaking in an anomalous diffusion process of mixed origins the ergodicity breaking parameter is a measure for the heterogeneity among different trajectories of one ensemble in this report this parameter is calculated for fractional brownian motion with a random change of time scale often called subordination we show that this quantity is the same as the known continuous time random walks case

computing reliability indices of repairable systems via signature the purpose of this paper is to show the usefulness of system signature for computing some important reliability indices of repairable systems in particular we obtain signature based expressions for stationary availability rate of occurrence of failure and mean time to the first failure of repairable systems using these expressions we compute corresponding reliability indices of all systems with three and four components computational results are also presented for consecutive k within m out of n f and m consecutive k out of n f systems

estimation of parameters of the shifted gompertz distribution using least squares maximum likelihood and moments methods nonlinear least squares procedures for estimating the parameters of the shifted gompertz distribution are proposed simulation studies are carried out to compare weighted and unweighted least squares methods the maximum likelihood method and method of moments this work concludes that least squares methods via weighting factors to estimate the parameters of this probability distribution give a better performance than unweighted least squares methods showing the importance of weighting factors besides results of this simulation study show that a good performance is obtained using the maximum likelihood method and the estimators obtained with more bias are those of the method of moments

estimating parameters in continuous univariate distributions with a shifted origin summary a general method of estimating parameters in continuous univariate distributions is proposed it is especially suited to cases where one of the parameters is an unknown shifted origin this occurs for example in the three parameter lognormal gamma and weibull models for such distributions it is known that maximum likelihood ml estimation can break down because the likelihood is unbounded and this can lead to inconsistent estimators properties of the proposed method are described in particular it is shown to give consistent estimators with asymptotic efficiency equal to ml estimators when these exist moreover it gives consistent asymptotically efficient estimators in situations where ml fails examples are given including numerical ones showing the advantages of the method

on the existence of asymptotically decaying positive solutions of second order neutral differential equations abstract the existence of positive solutions of second order neutral differential equation x t cx t p t x g t 0 t t0 is investigated some sufficient conditions are given for the existence of positive solutions with asymptotic decay of for the cases of constant sign and nonconstant sign of coefficients it also is shown that one of these sufficient conditions is necessary

asymptotically polynomial solutions to difference equations of neutral type asymptotic properties of solutions to difference equation of the form m x n u n x n k a n f n x n b n are studied we give sufficient conditions under which all solutions or all solutions with polynomial growth or all nonoscillatory solutions are asymptotically polynomial we use a new technique which allows us to control the degree of approximation

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

density estimation with confidence sets exemplified by superclusters and voids in the galaxies abstract a method is presented for forming both a point estimate and a confidence set of semiparametric densities the final product is a three dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters the boundaries of the smoothing parameter are determined by a nonparametric goodness of fit test that is based on the sample spacings for each value of the smoothing parameter our estimator is selected by choosing the normal mixture that maximizes a function of the sample spacings a point estimate is selected from this confidence set by using the method of cross validation an algorithm to find the mixing distribution that maximizes the spacings functional is presented these methods are illustrated with a data set from the astronomy literature the measurements are velocities at which galaxies in the corona borealis region are moving away from our galaxy if the galaxies are clustered the velocity density will be multimodal with clusters correspond

statistical analysis for geometric distribution based on records in this paper based on records from the geometric distribution non bayesian and bayesian estimators for the unknown parameter are obtained the empirical bayes estimate is derived using the squared error loss function the admissibility of estimators are discussed also the problem of predicting the future record values either point or interval based on the past record values observed is considered from bayesian and non bayesian approaches

maximum likelihood estimation of parameters in the inverse gaussian distribution with unknown origin maximum likelihood estimation is applied to the three parameter inverse gaussian distribution which includes an unknown shifted origin parameter it is well known that for similar distributions in which the origin is unknown such as the lognormal gamma and weibull distributions maximum likelihood estimation can break down in these latter cases the likelihood function is unbounded and this leads to inconsistent estimators or estimators not asymptotically normal it is shown that in the case of the inverse gaussian distribution this difticulty does not arise the likelihood remains bounded and maximum likelihood estimation yields a consistent estimator with the usual asymptotic normality properties a simple iterative method is suggested for the estimation procedure numerical examples are given in which the estimates in the inverse gaussian model are compared with those of the lognormal and weibull distributions

estimation of parameters of the gompertz distribution using the least squares method the gompertz distribution has been used to describe human mortality and establish actuarial tables recently this distribution has been again studied by some authors the maximum likelihood estimates for the parameters of the gompertz distribution has been discussed by garg et al j r statist soc c 19 1970 152 the purpose of this paper is to propose unweighted and weighted least squares estimates for parameters of the gompertz distribution under the complete data and the first failure censored data series systems see j statist comput simulat 52 1995 337 a simulation study is carried out to compare the proposed estimators and the maximum likelihood estimators results of the simulation studies show that the performance of the weighted least squares estimators is acceptable

fractional langevin equation we investigate fractional brownian motion with a microscopic random matrix model and introduce a fractional langevin equation we use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath we further compare fractional brownian motion with the fractal time process the respective mean square displacements of these two forms of anomalous diffusion exhibit the same power law behavior here we show that their lowest moments are actually all identical except the second moment of the velocity this provides a simple criterion that enable us to distinguish these two non markovian processes

corrected maximum likelihood in non regular problems on suggere que l utilisation du produit des densites pour la fonction de vraisemblance est une mauvaise application de la methode du maximum de vraisemblance dans des cas non reguliers