Showing papers on "Natural exponential family published in 1995"
TL;DR: The exponential generalized beta distribution (EGB) as discussed by the authors is a five-parameter beta distribution which nests the generalized beta and gamma distributions and includes more than thirty distributions as limiting or special cases.
455 citations
TL;DR: This paper proposes possibility regression analysis which is suitable for rough phenomena arising from social and economic systems and can be directly transferred into the exponential possibility distribution of coefficients in the regression model by the proposed method.
100 citations
TL;DR: In this article, it was shown that the form of the standard conjugate distribution for the mean parameter μ of a univariate natural exponential family F coincides with that of the distribution induced on μ by the canonical parameter if and only if F has a quadratic variance function.
Abstract: Recently, Consonni and Veronese have shown that the form of the standard conjugate distribution for the mean parameter μ of a univariate natural exponential family F coincides with that of the distribution induced on μ by the standard conjugate distribution for the canonical parameter if and only if F has a quadratic variance function. In this article we present significant extensions of this result, identifying conditions under which transformations of the canonical or mean parameter preserve the form of the standard conjugate family. Generalizations to the multivariate case are also considered, and results relating Jeffreys's prior to the standard conjugate family are presented. The variance function is seen to play an important role throughout.
37 citations
TL;DR: In this article, a functional equation of the form f(x + u) = F(x) F(u) for all (x, u) ∈ S, with S = R2n+ is defined, which expresses a complete lack of memory that is possessed only by distributions with independent exponential marginals.
21 citations
TL;DR: In this article, a generalised three-parameter gamma distribution was fitted to three creep failure data sets obtained from BSCC and confidence limits for 50, 10% and 1% quantiles of log failure time were computed using distributions most and least supported by the data.
19 citations
17 citations
TL;DR: In this article, the authors considered the discrete distribution family with the property p n (a,b) = h 1 n b + h 2 n p n - 1 (a + b,b), n = 1,2,…, with p 0(a, b) = exp(−a) to obtain a recursive formula for computing the distribution function of the compound generalized Poisson distribution.
Abstract: Ambagaspitiya and Balakrishnan (1994a) used the identity p n (a,b) = a a + b b + a n p n - 1 (a + b,b), n = 1,2,…, with p0(a, b) = exp(−a) to obtain a recursive formula for computing the distribution function of the compound generalized Poisson distribution. In this paper, we consider the discrete distribution family with the property p n (a,b) = h 1 (a,b) + h 2 (a,b) n p n - 1 (a + b,b), n = 1,2,…, which is a generalization of the first identity. We prove that weighted generalized Poisson distributions and weighted generalized negative binomial distributions with weights of the form w(a + bn; b) are two subclasses in the family. We provide a recursive formula for computation of respective compound distributions. Also we discuss the stability of the recursion as well as handling overflow / underflow problems.
10 citations
TL;DR: In this article, a general characterization theorem based on conditional expectation is proved for the exponential class of distributions, which is then applied to numerous discrete and continuous probability distributions, providing specific characterizations for each one of them.
Abstract: A general characterization theorem, based on conditional expectation, is proved for the exponential class of distributions. The theorem is then applied to numerous discrete and continuous probability distributions of the exponential class providing specific characterizations for each one of them. >
10 citations
IBM1
TL;DR: In this article, a general approach for calculating instantaneous availability is presented, which is applicable to systems or subsystems which are assumed to be returned to approximately their original state upon the completion of repair.
Abstract: Most current state-of-the-art availability models are based on continuous-time Markov chains. This involves restrictive assumption about the probability distribution for both failure times and repair times being exponential. In many situations, the exponential distribution is not applicable for failure times and/or repair times. A general approach for calculating instantaneous availability is presented. It is applicable to systems or subsystems which are assumed to be returned to approximately their original state upon the completion of repair. It is based on the equation: A(t)=R(t)+/spl int//sup t//sub 0/R(t-s)m(s)ds. The first case study is a validation study since the uptimes and downtimes are both assumed to follow an exponential distribution. In this case, an analytical result for A(t) can be obtained. Thus, the results for the analytical approach and the proposed approach can be compared. An analysis of the results shows the proposed approach to be very reasonable. In the second case study, the uptimes are assumed to follow a Weibull distribution while the downtimes have a lognormal distribution.
10 citations
9 citations
TL;DR: In this article, the authors considered a problem of selecting a best k one parameter exponential families with quadratic variance functions which is associated with the largest mean and showed that the minimax value under the "0-1" loss function is 1 − 1/k.
TL;DR: In this paper, the authors describe a method due to Lindsey (1974a) for fitting different exponential family distributions for a single population to the same data, using Poisson log-linear modelling of the density or mass function.
Abstract: This paper describes a method due to Lindsey (1974a) for fitting different exponential family distributions for a single population to the same data, using Poisson log-linear modelling of the density or mass function. The method is extended to Efron's (1986) double exponential family, giving exact ML estimation of the two parameters not easily achievable directly. The problem of comparing the fit of the non-nested models is addressed by both Bayes and posterior Bayes factors (Aitkin, 1991). The latter allow direct comparisons of deviances from the fitted distributions.
TL;DR: In this article, an asymptotically optimal test for testing the appropriateness of a fixed effects model versus a random effects model for the exponential family based independent data was developed.
Abstract: Recently exponential family based random effects models have received considerable attention. These models usually arise from an unobservable random process added to the independent exponential family models. An unobservable correlated process, however, would cause correlations among the exponential family based data. This paper, first, develops an asymptotically optimal test for testing the appropriateness of a fixed effects model for the exponential family based independent data versus a random effects model for the exponential family based independent or correlated data. The paper, then, provides a general framework on regression analysis for the exponential family based data generated under the random effects models.
01 Jul 1995
TL;DR: This paper examines the method of moments as a general estimation technique for estimating the parameters of the component distributions and their mixing proportions and shows that the same basic solution can be applied to any continuous or discrete density from the exponential family with a known common shape parameter.
Abstract: A finite mixture distribution consists of the superposition of a finite number of component probability densities, and is typically used to model a population composed of two or more subpopulations Mixture models find utility in situations where there is a difficulty in directly observing the underlying components of the population of interest This paper examines the method of moments as a general estimation technique for estimating the parameters of the component distributions and their mixing proportions It is shown that the same basic solution can be applied to any continuous or discrete density from the exponential family with a known common shape parameter Results of an empirical study of the method are also presented >
TL;DR: Yanushkevichius and Mokslas as mentioned in this paper reviewed the results obtained in the last three years and investigated the stability of characterization of the exponential law by regression properties of order statistics.
Abstract: The stability of characterizations of the exponential distribution came to the attention of many authors. The main achievements in that sphere up to1990 are given in the author's monograph [R. Yanushkevichius,Stability of Characterizations of Probability Distributions, Mokslas, Vilnius, (1991)]. In the present paper we review the results obtained in the last three years and investigate the stability of characterization of the exponential law by regression properties of order statistics.
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TL;DR: In this paper, a class of natural exponential family of distributions having power variance function is considered and an appropriate sequential procedure for estimating the mean μ of under a combined loss of weighted estimation error and sampling cost is proposed.
Abstract: Let denote the class of natural exponential family of distributions having power variance function. An appropriate sequential procedure for estimating the mean μ of under a combined loss of weighted estimation error and sampling cost is proposed. The usual estimator, namely , where t is an appropriate stopping time, is shown to be biased. To remedy this deficiency, we propose a class of estimators to correct for the bias. The asymptotic properties of the suggested estimators are provided. In particular, one realizes the tradeoff between the bias reduction and the reduced regret compared to the ususal estimator.
01 Jan 1995
01 Jan 1995
TL;DR: Algorithms for the generation of pseudorandom numbers with normal and exponential distributions are described here, which are much faster than other exponential and normal random number generators.
Abstract: Algorithms for the generation of pseudorandom numbers with normal and exponential distributions are described here. No transcendental functions need to be evaluated; furthermore, only two uniform deviates per generation are required; no tables are used. These algorithms are much faster than other exponential and normal random number generators.
TL;DR: In this paper, an accelerated version of the full purely sequential methodology of Bose and Boukai (1993b, submitted) is proposed along the lines of Mukhopadhyay (1993a, Tech Report, No 93-27, Department of Statistics, University of Connecticut) in order to achieve operational savings.
Abstract: The minimum risk point estimation for the mean is addressed for a natural exponential family (NEF) that also has a power variance function (PVF) under a loss function given by the squared error plus linear cost An appropriate accelerated version of the full purely sequential methodology of Bose and Boukai (1993b, submitted) is proposed along the lines of Mukhopadhyay (1993a, Tech Report, No 93-27, Department of Statistics, University of Connecticut) in order to achieve operational savings The main result provides the asymptotic second-order expansion of the regret function associated with the accelerated sequential estimator of the population mean
01 Jan 1995
TL;DR: In this paper, a differential geometric framework in Euclidean space for exponential family nonlinear models is presented, and some asymptotic inference related to statistical curvatures and Fisher information are studied.
Abstract: A differential geometric framework in Euclidean space for exponential family nonlinear models is presented. Based on this framework, some asymptotic inference related to statistical curvatures and Fisher information are studied. This geometric framework can also be extended to more genera) dass of models and used to study some other problems.
TL;DR: In this article, simple formulas for an approximate evaluation of distribution functions belonging to the class of exponential distributions with the exponent ranging between 1 and 7.5 are presented, and errors of approximations for integer-valued and some fractional exponents are provided.
Abstract: Simple formulas for an approximate evaluation of distribution functions belonging to the class of exponential distributions with the exponent ranging between 1 and 7.5 are presented. Errors of approximations for integer-valued and some fractional exponents are provided.