information measures for generalized gamma family the objective of this paper is to integrate the generalized gamma gg distribution into the information theoretic literature we study information properties of the gg distribution and provide an assortment of information measures for the gg family which includes the exponential gamma weibull and generalized normal distributions as its subfamilies the measures include entropy representations of the log likelihood ratio aic and bic discriminating information between gg and its subfamilies a minimum discriminating information function power transformation information and a maximum entropy index of fit to histogram we provide the full parametric bayesian inference for the discrimination information measures we also provide bayesian inference for the fit of gg model to histogram using a semi parametric bayesian procedure referred to as the maximum entropy dirichlet med the gg information measures are computed for duration of unemployment and duration of ceo tenure

maximum tsallis entropy with generalized gini and gini mean difference indices constraints abstract using the maximum entropy principle with tsallis entropy some distribution families for modeling income distribution are obtained by considering income inequality measures maximum tsallis entropy distributions under the constraint on generalized gini and gini mean difference indices are derived it is shown that the tsallis entropy maximizers with the considered constraints belong to generalized pareto family

a new concept of relative suitability of moment function sets in modeling statistical data by using entropy optimization distributions the choice of a suitable moment function set and various combinations of their elements are very important it is also important to have criteria to compare various moment sets for suitability considering this in the present study by choosing special moment function sets we have obtained maxmaxent minmaxent distributions and shown that the minmaxent distribution more exactly represents the given statistical data moreover in order to compare various moment function sets for suitability we have suggested a new concept of relative suitability of moment function sets for given statistical data and the importance of this concept has been presented in some applications using real data

product formulas for the cyclotomic v schur algebra and for the canonical bases of the fock space abstract let f q s be the q deformed fock space of level l with multi charge s s 1 s l uglov defined canonical bases g s of f q s for l partitions and the polynomials q z q are defined as the coefficients of the transition matrix between the canonical bases and the standard basis of f q s in this paper we prove a product formula for q for certain l partitions which expresses q as a product of such polynomials related to various smaller fock spaces f q s i yvonne conjectures that q are related to the q decomposition numbers d q of the cyclotomic v schur algebra s where the parameters v q 1 q l are roots of unity in c determined from s in our earlier work we have proved a product formula for d q of s and the product formula for q is regarded as a counter part of that formula for the case of the fock space

on the mullineux involution for ariki koike algebras abstract this note is concerned with a natural generalization of the mullineux involution for ariki koike algebras by using a result of fayers together with previous results by the authors we give an efficient algorithm for computing this generalized mullineux involution our algorithm notably does not involve the determination of paths in affine crystals

on the category o for rational cherednik algebras we study the category o of representations of the rational cherednik algebra aw attached to a complex reflection group w w e construct an exact functor called knizhnik zamolodchikov functor o hw mod where hw is the finite iwahori hecke algebra associated to w we prove that the knizhnik zamolodchikov functor induces an equiv alence between o otor the quotient of o by the subcategory of aw modules supported on the discriminant and the category of finite dimensional hw modules the standard aw modules go under this equivalence to certain modules arising in kazhdan lusztig theory of cells provided w is a weyl group and the hecke algebra hw has equal parameters we prove that the category o is equivalent to the module category over a finite dimensional algebra a generalized q schur algebra associated to w

parabolic kazhdan lusztig polynomials and schubert varieties abstract we shall give a description of the intersection cohomology groups of the schubert varieties in partial flag manifolds over symmetrizable kac moody lie algebras in terms of parabolic kazhdan lusztig polynomials introduced by deodhar

additional criteria in fuzzy two level pattern recognition abstract pattern recognition with fuzzy sets is considered with regard to medical diagnostic problems an alternative interpretation of membership grade is suggested which expresses the degree of illness of a patient with respect to a certain disease a formal statement of a two level fuzzy classifier is presented the main emphasis is put on additional criteria designed to evaluate a fuzzy diagnostic decision for an unknown object two groups of criteria are formed decision making connected and domain dependent the decision making group of criteria can be viewed as related to the soft consensus measure in group decisions theory interconnections between criteria are discussed the notions proposed are illustrated with real medical data from the fields of aviation medicine and neonatology

a general functional form for approximating the lorenz curve abstract the purpose of this paper is to present several descriptive approximations of empirical lorenz curves each of these hypothetical forms is less restrictive than those considered before we compare these alternative forms by goodness of fit f tests of nested forms and measurement of the gini coefficient

elliptical lorenz curves abstract a family of elliptic lorenz curves is proposed for fitting grouped income data the associated distribution and density functions are displayed together with the gini indices estimation procedures are discussed comparisons are made with alternative models using australian 1967 68 income data

generalized entropy optimization problems and the existence of their solutions abstract in the present study we have formulated a generalization of entropy optimization problems geop proposed sufficient conditions for the existence of solution we have suggested also a new method based on a priori evaluations and newton s methods for calculation of langrange multipliers mentioned method allows calculating langrange multipliers by starting from arbitrary initial point for newton s approximations of constructed auxiliary equation the solution of auxiliary equation is chosen as initial point for second constructed auxiliary equation the recurring mentioned process for finite time leads to achieve an initial point for newton s approximations of given equation and allows to find its unknown solution

a valuation of state of object based on weighted mahalanobis distance abstract a method of valuation of the state of a multidimensional object is presented the considered object may be described by continuous and discrete variables as well the method consists in evaluating the weighted mahalanobis distance between the object and a multidimensional norm estimate this distance can be standardized to take the values from the interval 0 1

some generalized functions for the size distribution of income many distributions have been used as descriptive models for the size distribution of income this paper considers two generalized beta distributions which include many of these models as special or limiting cases these generalized distributions have not been used as models for the distribution of income and provide a unified method of comparing many models previously considered

a comparison of q decomposition numbers in the q deformed fock spaces of higher levels abstract the q deformed fock spaces of higher levels were introduced by jimbo misra miwa and okado the q decomposition matrix is a transition matrix from the standard basis to the canonical basis defined by uglov in the q deformed fock space in this paper we show that parts of q decomposition matrices of level l coincide with that of level l 1 under certain conditions of multicharge

entropy and predictability of stock market returns abstract we examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties we compare our results with a number of traditional measures the metric entropy is capable of detecting nonlinear dependence within the returns series and is also capable of detecting nonlinear affinity between the returns and their predictions obtained from various models thereby serving as a measure of out of sample goodness of fit or model adequacy several models are investigated including the linear and neural network models as well as nonparametric and recursive unconditional mean models we find significant evidence of small nonlinear unconditional serial dependence within the returns series but fragile evidence of superior conditional predictability profit opportunity when using market switching versus buy and hold strategies

the jantzen sum formula for cyclotomic schur algebras the cyclotomic q schur algebra was introduced by dipper james and mathas in order to provide a new tool for studying the ariki koike algebra we here prove an analogue of jantzen s sum formula for the cyclotomic q schur algebra among the applications is a criterion for certain specht modules of the ariki koike algebras to be irreducible

fuzzy characterization of coronary disease abstract the paper presents a methodology based on fuzzy set theory to study the influence of social and psychological factors on the coronary disease a life history questionnaire has been used to collect data from control subjects and coronary patients the two groups made homogeneous in respect to objective features like sex age job etc have been used as training sets to learn the most relevant combinations of social and psychological features in the characterization of the coronary disease each of these features like stress social mobility hysteria etc is represented by means of a fuzzy linguistic variable whose membership value is evaluated on the basis of the answers to the questions relative to the particular feature

relationships between some notions which are common to reliability theory and economics our objective in writing this paper is to point out some interesting relationships between the commonly referred to indices of economic inequality and a central notion used in reliability theory specifically we show that the lorenz curve and the gini index of economics are related to the total time on test and the mean residual life of reliability theory an advantage of observing these relationships is that we are now able to consolidate knowledge that has independently evolved in two apparently diverse areas and furthermore we are able to show that a recently proposed test for exponentiality based on the gini index is identical to the one based on the total time on test obtain some new inequalities for the lorenz curve the gini index and the redundancy which is another measure of economic inequality present some preservation properties for the lorenz curve which do not appear to be known suggest that the lorenz curve can be used to obtain a different interpretation of lifetime data and characterize the limit of a class of lifetime distributions with decreasing failure rate in terms of its lorenz curve

cellular structures on hecke algebras of type b abstract the aim of this paper is to gather and try to unify several approaches for the modular representation theory of hecke algebras of type b we attempt to explain the connections between geck s cellular structures coming from kazhdan lusztig theory with unequal parameters and ariki s theorem on the canonical basis of the fock spaces

estimation of lorenz curves a bayesian nonparametric approach abstract in this article we estimate lorenz curves using the recent development of the bayesian nonparametric method with dirichlet process prior we also consider contaminated observations of income and propose a method for removing these contaminated observations further we present examples using both simulated data and real data to illustrate our approach

models prior information and bayesian analysis abstract formulation of models for observations and prior densities for their parameters is an important activity in many sciences in the present paper after a discussion of this area of activity entropy based methods are employed to derive many central econometric and statistical models and noninformative and informative prior densities for their parameters in an explicit reproducible manner examples are provided to illustrate the general procedures in particular maxent is employed to produce linear and nonlinear regression and autoregression models hierarchical models time varying parameter models etc then maximal data information prior mdip densities for hyperparameters common parameters in different likelihood functions multinomial parameters etc are derived also the mdip approach is utilized to produce prior odds for alternative hypotheses or models

an ordered family of lorenz curves abstract a general method for building parametric functional families of lorenz curves generated from an initial lorenz curve which satisfies some regularity conditions is presented it is shown that these families can be ordered in a manner which leads to a hierarchy of lorenz curves the method starts from a generating lorenz curve l 0 p and builds the family by increasing the number of parameters which can be easily interpreted in terms of the elasticities of l 0 p the method is applied to a family we term the pareto family since they use the pareto lorenz curves as their generating curves the family is shown to contain an important number of classical lorenz curves used in the existing literature several properties of this family are analyzed these include the population function inequality measures and lorenz orderings a general method for the estimation of these family is given and applied to the pareto family finally an application is presented for data from various countries the results are very robust across data sources the pareto models fit very well in a number of applications

on the generalized cumulative residual entropy with applications in actuarial science recently psarrakos and navarro 2013 proposed a new measure of uncertainty which extends the cumulative residual entropy cre called the generalized cumulative residual entropy gcre in the present paper new properties and applications in actuarial risk measures of the gcre are explored bounds stochastic order properties and characterization results of the new entropy are also discussed it is shown that the gcre is invariant under changes in location and scale directly with scale of a random variable the same properties also hold for the standard deviation it is also proved that the gcre of the first order statistics can uniquely determine the parent distribution the weibull distribution which is commonly used in several fields of applied probability is characterized by using the mentioned generalized measure the gcre is studied as a risk measure and is compared to the standard deviation and the right tail risk measure where the latter measure was introduced by wang 1998 several examples are also given to illustrate the new results

a bayesian approach to diagnosis of asset pricing models a large literature has arisen which exploits a particular portfolio on the mean variance frontier determining a minimum variance bound on the set of stochastic discount factors state price to probability ratios this paper proposes a new variational characterization of the closely related set of state price densities based on minimization of the kullback leibler information criterion in contrast to the variance bound the resulting information bound automatically satisfies an important positivity constraint furthermore the information bound is determined by a portfolio which maximizes expected cara utility several interpretations of the information bound are given and empirical uses of it are illustrated

james s conjecture holds for weight four blocks of iwahori hecke algebras abstract james s conjecture suggests that in certain cases the decomposition numbers for the iwahori hecke algebra of the symmetric group over a field of prime characteristic and in particular the decomposition numbers for the symmetric group itself coincide with the decomposition numbers for a corresponding iwahori hecke algebra defined over c and hence can be computed using the llt algorithm we prove this conjecture for blocks of weight 4

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

maximum entropy in the problem of moments the maximum entropy approach to the solution of underdetermined inverse problems is studied in detail in the context of the classical moment problem in important special cases such as the hausdorff moment problem we establish necessary and sufficient conditions for the existence of a maximum entropy solution and examine the convergence of the resulting sequence of approximations a number of explicit illustrations are presented in addition to some elementary examples we analyze the maximum entropy reconstruction of the density of states in harmonic solids and of dynamic correlation functions in quantum spin systems we also briefly indicate possible applications to the lee yang theory of ising models to the summation of divergent series and so on the general conclusion is that maximum entropy provides a valuable approximation scheme a serious competitor of traditional pade like procedures

new classes of lorenz curves by maximizing tsallis entropy under mean and gini equality and inequality constraints abstract in this paper by using the entropy maximization principle with tsallis entropy new distribution families for modeling the income distribution are derived also new classes of lorenz curves are obtained by applying the entropy maximization principle with tsallis entropy under mean and gini index equality and inequality constraints

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

maximum entropy and the problem of moments a stable algorithm we present a technique for entropy optimization to calculate a distribution from its moments the technique is based upon maximizing a discretized form of the shannon entropy functional by mapping the problem onto a dual space where an optimal solution can be constructed iteratively we demonstrate the performance and stability of our algorithm with several tests on numerically difficult functions we then consider an electronic structure application the electronic density of states of amorphous silica and study the convergence of the fermi level with increasing number of moments

calculation of maximum entropy densities with application to income distribution the maximum entropy approach is a flexible and powerful tool for density approximation this paper proposes a sequential updating method to calculate the maximum entropy density subject to known moment constraints instead of imposing the moment constraints simultaneously the sequential updating method incorporates the moment constraints into the calculation from lower to higher moments and updates the density estimates sequentially the proposed method is employed to approximate the size distribution of u s family income empirical evidence demonstrates the efficiency of this method

the representation type of hecke algebras of type b abstract this paper determines the representation type of the iwahori hecke algebras of type b when q 1 in particular we show that a single parameter non semisimple iwahori hecke algebra of type b has finite representation type if and only if q is a simple root of the poincare polynomial confirming a conjecture of uno s j algebra 149 1992 287

ordering univariate distributions by entropy and variance this paper examines the role of variance and entropy in ordering distributions and random prospects there is no universal relation between entropy and variance orderings of distributions but we place their relationship in the context of a stronger ordering relation known as dispersion ordering further some conditions are identified under which variance and entropy order similarly when continuous variables are transformed we also analyze parametric changes which do not disturb the agreement between these rankings the results are conveniently tabulated in terms of distribution parameters

new functional forms of lorenz curves by maximizing tsallis entropy of income share function under the constraint on generalized gini index abstract the lorenz curve is one of the most powerful tools in the analysis of the size distribution of income and wealth in the past decades many authors have proposed different functional forms for estimating lorenz curves using a variety of approaches in this paper new functional forms are derived by maximizing tsallis entropy of income share function subject to a given generalized gini index the obtained lorenz curves are fitted to the income data sets of three asian countries in 1988 and their relative performances with respect to some well known parametric models of lorenz curves are compared using two types of goodness of fit measures

a conjecture for q decomposition matrices of cyclotomic v schur algebras abstract the jantzen sum formula for cyclotomic v schur algebras yields an identity for some q analogues of the decomposition matrices of these algebras we prove a similar identity for matrices of canonical bases of higher level fock spaces we conjecture then that those matrices are actually identical for a suitable choice of parameters in particular we conjecture that decomposition matrices of cyclotomic v schur algebras are obtained by specializing at q 1 some transition matrices between the standard basis and the canonical basis of a fock space

cyclotomic double affine hecke algebras and affine parabolic category o using the orbifold kz connection we construct a functor from an affine parabolic category o of type a to the category o of a cyclotomic rational double affine hecke algebra h then we give several results concerning this functor

a note on the usefulness of linguistic variables for differentiating between some respiratory diseases abstract an uncommon application of linguistic variables as predictor variables for obtaining classical discriminant functions is presented commonly only quantitative features are used as predictor variables for evaluating linear quadratic or canonical discriminant functions because of the assumption of normality this paper deals with results of discrimination between various respiratory diseases using quantitative and linguistic variables together linguistic variables in medical applications were obtained by saitta and torasso fuzzy sets and systems 5 1981 245 258 as a conversion of the groups of original discrete features the classical linear quadratic and canonical discriminant functions were calculated for our data to make a trial of automatical diagnosis we obtain a considerable amelioration of the results of discrimination using the complete set of variables quantitative and linguistic instead of only quantitative ones the percentage of correctly classified patients increased from 86 to 97 percent in the case of linear discriminant function the variables with the greatest discriminative power were also chosen these were the linguistic variables character of dyspnoea physical examination of the chest and x ray examination of the chest the presented method enables the simultaneous use of quantitative and qualitative features to the description of the patient s state for this reason linguistic variables seem to be an efficient tool in medical applications

explicit expressions of the pietra index for the generalized function for the size distribution of income abstract the importance of the pietra index in socioeconomic systems and econophysics has been highlighted by eliazar and sokolov 2010 in this paper we obtain closed expressions for the pietra index for the generalized function for the size of income proposed by mcdonald 1984 this family is composed of three classes of distributions the generalized gamma distribution gg the generalized beta of the first kind gb1 and the generalized beta of the second kind gb2 for the different distributions we obtain closed and simple expressions of the pietra index which can be easily computed we also obtain the pietra index for other relevant income models including finite mixtures of distributions and the generalized distribution clementi et al 2008 finally two empirical applications with real income data are given

on a higher level extension of leclerc thibon product theorem in q deformed fock spaces abstract the q deformed fock spaces of higher levels were introduced by jimbo misra miwa okado uglov defined a canonical bases in q deformed fock spaces of higher levels leclerc thibon showed a product theorem in q deformed fock spaces of level one the product theorem is regarded as a formal q analogue of the tensor product theorem of level one in this paper we show a higher level analogue of leclerc thibon product theorem under a suitable multi charge condition

two flexible functional form approaches for approximating the lorenz curve abstract this paper introduces two flexible form approaches to approximate lorenz curves the first approach expands the inverse function of an income distribution in an exponential polynomial series and derives the lorenz curve from it the required convexity condition can be imposed using a bayesian method the second approach approximates the lorenz curve with a sequence of berstein polynomial functions the required convexity condition is automatically established in this approach we compare these approaches with other well known fixed functional form approaches we evaluate the performance of these functional forms by comparing approximation errors maximum error and the estimates of the gini coefficient produced by various approaches

entropy expressions and their estimators for multivariate distributions entropy expressions for several continuous multivariate distributions are derived point estimation of entropy for the multinormal distribution and for the distribution of order statistics from d g weinman s ph d dissertation ariz state univ tempe az 1966 exponential distribution is considered the asymptotic distribution of the uniformly minimum variance unbiased estimator for multinormal entropy is obtained simulation results on convergence of the means and variances of these estimators are provided

an alternative method for modeling the size distribution of top wealth abstract the pareto distribution has been widely applied in modeling the distribution of wealth as well as top incomes cities and firms however recent evidence has shown that the pareto distribution is not consistent with many situations in which it was previously considered applicable we propose an alternative method for estimating the upper tail distribution of wealth and suggest a new lorenz curve for building models to provide such estimates applying our new models to the forbes world s billionaire lists we show that they significantly outperform the pareto lorenz curve as well as some other popular alternatives

maximum entropy lorenz curves abstract for describing the distribution of income a family of maximum entropy density functions is derived under optional side conditions on the distance of the mean income from the minimum income and the absolute gini index of concentration many of the resulting lorenz curves obtained from the reciprocal of the density function by repeated quadrature turn out to be well known models

categorifications and cyclotomic rational double affine hecke algebras varagnolo and vasserot conjectured an equivalence between the category mathcal o for crdaha s and a subcategory of an affine parabolic category o of type a we prove this conjecture as applications we prove a conjecture of rouquier on the dimension of simple modules of crdaha s and a conjecture of chuang miyachi on the koszul duality for the category mathcal o of crdaha s