Natural exponential family

About: Natural exponential family is a research topic. Over the lifetime, 1973 publications have been published within this topic receiving 60189 citations. The topic is also known as: NEF.

A Survey of Tables of Probability Distributions.

Abstract: This article is a survey of the tables of probability distributions published about or after the publication in 1964 of the Handbook of Mathematical Functions, edited by Abramowitz and Stegun

Semi Tail Upper Bounds on the Class of Admissible Estimators in Discrete Exponential Families with Applications to Poisson and Negative Binomial Distributions

Abstract: Admissibility problems involving simultaneous estimation in discrete exponential families are studied by solving difference inequalities. It is shown that if an estimator is admissible under the loss function $L_m(\mathbf{\theta, a)} = \sum^p_{i = 1} \theta^{m_i}_i (\theta_i - a_i)^2$, then in the tail (i.e., for large values of the observations), this estimator has to be less than certain bounds. Specific bounds, called Semi Tail Upper Bounds (STUB), are given here. These STUBs are not only of theoretical interest, but also are sharp enough that they establish many new results. Two of the most interesting ones are: (i) the establishment of Brown's conjecture concerning inadmissibility of some of the estimators proposed by Clevenson and Zidek (1975), and (ii) the establishment of inadmissibility of Hudson's (1978) estimator which improves upon the uniformly minimum variance unbiased estimator in Negative Binomial families.

Differential Relations, in the Original Parameters, which Determine the First Two Moments of the Multiparameter Exponential Family

Abstract: We study general multiparameter exponential families of distribution and obtain differential equations relating the first two moments of the sufficient statistics to the normalization constant. Another result illuminates the structure of both the second order partial derivatives of the likelihood and their expected values.

Tauber theory for infinitely divisible variance functions

Abstract: We study a notion of Tauber theory for infinitely divisible natural exponential families, showing that the variance function of the family is (bounded) regularly varying if and only if the canonical measure of the Levy-Khinchine representation of the family is (bounded) regularly varying. Here a variance function V is called bounded regularly varying if V(μ)\sim cμp either at zero or infinity, with a similar definition for measures. The main tool of the proof is classical Tauber theory.

Weibull Generalized Exponential Distribution

Abstract: This paper introduces a new three-parameters model called the Weibull-G exponential distribution (WGED) distribution which exhibits bathtub-shaped hazard rate. Some of it's statistical properties are obtained including quantile, moments, generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.