Showing papers on "Natural exponential family published in 1988"
TL;DR: In this paper, the authors consider a general class of bivariate distributions such that both sets of conditional densities are exponential, where the joint density must be proportional to exp(- λx - μy - νxy), where the constant of proportionality depends on the classical exponential integral.
Abstract: It is frequently easier to visualize conditional distributions of experimental variables rather than joint distributions. In this article we consider the most general class of bivariate distributions such that both sets of conditional densities are exponential. The class proves to be remarkably simple to describe: The joint density must be proportional to exp(- λx - μy - νxy), where the constant of proportionality depends on the classical exponential integral. The joint distribution has marginals that are not exponential and a negative correlation coefficient, except in the special case of independence. After deriving some distributional results, we develop methods for parameter estimation and simulation. A simple method-of-moments estimator appears to give reasonable results. We also briefly discuss generalizations to higher dimensions and to distributions with conditionals in a general exponential family.
151 citations
TL;DR: In this paper, des approximations precises and facilement calculables for les densites conditionnelles and les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques are developed.
Abstract: On developpe des approximations precises et facilement calculables pour les densites conditionnelles et les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques
87 citations
TL;DR: A survey of multivariate exponential distributions and their applications in reliability can be found in this paper, where the authors discuss the important multivariate extensions of the univariate exponential distribution, including the exponential marginals.
Abstract: Publisher Summary This chapter discusses the multivariate exponential distributions and their applications in reliability. The univariate exponential distribution is well known as a model in reliability theory. Because of the usefulness of the univariate exponential distribution it is natural to consider multivariate exponential distributions as models for multicomponent systems. However, there is no natural extension available in a unique way. The chapter presents a survey of bivariate exponential distributions, the important multivariate extensions, and discusses the important multivariate extensions. Initial attempts have been to obtain a bivariate exponential distribution with exponential marginals without any appealing physical interpretations. The chapter also discusses Gumbel's distributions, Freund's model, Marshall–Olkin model, Block–Basu model, Friday and Patil distribution, Downton distribution, and other bivariate distributions.
34 citations
TL;DR: In this paper, a family of multivariate symmetric distributions with i.i.d. components is introduced, denoted by Fn and studied from several aspects such as distribution functions, probability density functions, marginal and conditional distributions and components' independence.
32 citations
Journal Article•
TL;DR: In this paper, the conditions générales d'utilisation (http://www.compositio.org/conditions) of the agreement with the Foundation Compositio Mathematica are described.
Abstract: © Foundation Compositio Mathematica, 1988, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
27 citations
TL;DR: In this article, a one-parameter bivariate family of distributions whose marginals are arbitrary and which include Frechet bounds as well as the distribution corresponding to independent variables is introduced, and some geometrical and statistical properties on the stochastic dependence parameter are studied.
20 citations
TL;DR: In this article, tight bounds on the sup metric between the exponential distribution and new better (worse) than used in expectation (NBUE, NWUE) distributions are established in terms of the proximity of the second moments of the distributions concerned.
Abstract: Tight bounds on the sup metric between the exponential distribution and new better (worse) than used in expectation (NBUE, NWUE) distributions are established in terms of the proximity of the second moments of the distributions concerned. Real variable methods are used to identify the extremal distributions that attain the bounds. Similar methods establish similar results for the harmonic NBUE and NWUE classes of distributions.
15 citations
TL;DR: On considere deux exemples dans lesquels l'estimation du maximum de quasi-vraisemblance peut etre consideree comme une alternative viable a des methodes plus standards as discussed by the authors.
Abstract: On considere deux exemples dans lesquels l'estimation du maximum de quasi-vraisemblance peut etre consideree comme une alternative viable a des methodes plus standards
14 citations
TL;DR: In this article, the exponential rate of convergence of posterior distribution around the mode is established by using the generalized Laplace method, and an example is also given in the context of the mode of the posterior distribution.
Abstract: After the observations were observed, the posterior distribution under mild conditions becomes more concentrated in the neighbourhood of the mode of the posterior distribution as sample size n increase. In this paper, the exponential rate of convergence of posterior distribution around the mode is established by using the generalized Laplace method. An example is also given.
14 citations
02 Nov 1988
TL;DR: The Carlitz-Uchiyama bound for geometric BCH codes is thearest bound available for exponential sums and L functions, and bounds for traces of exponential sums, for points of coverings, and for trace equations are given.
Abstract: Gilles L a c h a u d 1 S u m m a r y I n t r o d u c t i o n 1. The equation Tq-T = a 2. The equation yq-y = f 3. The genus of coverings 4. Exponential sums and L functions 5. Bounds for traces of exponential sums, for n u m b e r of points of coverings, and for trace equations 6. Examples : coverings of the line 7. The Carlitz-Uchiyama bound for geometric BCH codes Bibliography Introduction
8 citations
TL;DR: In an index to the distributions of Mathematical Statistics published in 1961, Frank A. Haight as mentioned in this paper considered the following distribution: α − 1 exp (−xe a α −1 ) ∑ n=0 ∞ (n+1) n−1 (n!) 2 x n 1 (0, ∞) (x) d x for 0 for 0
TL;DR: In this article, it was shown that the Maxwell-Boltzmann distribution (exponential distribution) is the continuum limit of Bose-Einstein statistics, which is the same as the limit of the exponential distribution.
TL;DR: In this article, a family of multivariate distributions, which consists of scale mixtures of symmetrized Dirichlet distributions, is introduced, and the basic properties of this family such as stochastic representation, probability density functions, marginal and conditional distributions are studied.
Abstract: In this paper we introduce a family of multivariate distributions, which consists of scale mixtures of symmetrized Dirichlet distributions. This family is a symmetrization of multivariate Liouville distributions and contains the well-known spherically symmetric distributions as a special case. The basic properties of this family such as stochastic representation, probability density functions, marginal and conditional distributions and components' independence are studied. A criterion of the invariance of statistics is also given.
DOI•
01 Feb 1988
TL;DR: In this paper, the exponential smoothing methods of forecasting are rationalized in terms of a statistical state space model with only one primary source of randomness, and their link, in general terms, with the ARMA class of models (both stationary and nonstationary cases) is also explored.
Abstract: In this paper the exponential smoothing methods of forecasting are rationalized in terms of a statistical state space model with only one primary source of randomness. Their link, in general terms, with the ARMA class of models ( both stationary and nonstationary cases) is also explored.
TL;DR: In this paper, it was shown that if the convolution of n HNBUE distributions is exponential, then n-1 of the distributions are degenerate at zero and the other distribution is exponential.
Abstract: The authors show that if the convolution of n HNBUE distributions is exponential, then n-1 of the distributions are degenerate at zero and the other distribution is exponential. This result is also shown to hold for the wider HNBUE(3) class. The result extends similar results previously published for the IFRA and NBU cases. The authors conjecture that if a monotonic system formed with independent components has exponential life, it must be essentially a series system with exponential components. >
TL;DR: In this article, the problem of minimum variance unbiased estimation of the probability density function of a random variable belonging to an exponential family is considered, and the method of estimation proposed in this paper requires the solution of a certain integral equation.
Abstract: The problem of minimum variance unbiased estimation of the probability density function of a random variable belonging to an exponential family is considered. The method of estimation proposed in this paper requires the solution of a certain integral equation. For many probability distributions the solution of this equation is given by a known result in integral transform theory.
TL;DR: In this article, the authors considered the class of nature exponential families generated by stable distributions and obtained an explicit expression for the uniformly minimum variance unbiased estimator for the r-th cumlant, the density function, and the reliability function.
Abstract: The class of nature exponential families generated by stable distributions has been introduced in different contexts by several authors. Tweedie (1984) and Jorgensen (1987) studied this class in the context of generalized liner models and exponential dispersion models. Bar-Lev and Enis (1986) introduced this class in the context of the property of reproducibility in natural exponential families and Hougaard (1986) found the distributions in this class to be natural candidates for applications as survival distributions in life tables for heterogeneous populations. In this note, we consider such a class in the context of minimum variance unbiased estimation. For each family in this class, we obtain an explicit expression for the uniformly minimum variance unbiased estimator for the r-th cumlant, the density function, and the reliability function.
03 Jan 1988
TL;DR: Simulation results show, for example, that an element in a table of 30000 exponentially distributed elements can be found in less than 10 accesses on the average, without using any knowledge of the distribution.
Abstract: Some new improvements on the Interpolation search are presented. They yield an average-case performance within an additive constant from optimal for uniformly distributed elements. The method is much less sensitive to non-uniform distributions than Interpolation search, and will have almost O(lg lgn) behavior for many distributions. Simulation results show, for example, that an element in a table of 30000 exponentially distributed elements can be found in less than 10 accesses on the average, without using any knowledge of the distribution.
TL;DR: In this article, it was shown that when the components are identically distributed, then necessarily each component follows the gamma law, and the gamma decomposition theorem for Chi-squared distributed quadratic forms in normal variates was shown for strongly reproductive exponential models with affine dual foliations.
01 Sep 1988
01 Jan 1988
TL;DR: In this paper, an approximation for the nonasymptotic probability density of the maximum likelihood estimates of parameters in a curved exponential family dominated by the Lebesgue measure is presented.
Abstract: The paper presents an approximative expression for the non-asymptotic probability density of the maximum likelihood estimates of parameters in a curved exponential family dominated by the Lebesgue measure. A typical example is the gaussian non-linear regression. A matrix in this expression is considered a possible alternative to the estimate of the Fisher information matrix in nonlinear models. The approach is differential-geometrical and the level of the approximation of the probability density is expressed in geometrical terms.