Topic
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.
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1 citations
01 Mar 1980
TL;DR: In this article, a first-order stochastic difference equation with random coefficients is shown to have a solution which makes the marginal distribution of the stationary sequence generated by the equation a convex mixture of two exponential distributions.
Abstract: : A first-order stochastic difference equation with random coefficients is shown to have a solution which makes the marginal distribution of the stationary sequence generated by the equation a convex mixture of two exponential distributions. This Markovian process should be broadly applicable in stochastic modelling in operations analysis. Moreover it can be extended quite simply to a mixed exponential process with mixed pth-order autoregressive and qth-order moving average correlation structure. Coupling of the processes to model multivariate situations is also discussed. (Author)
1 citations
Dissertation•
01 Jan 2010
TL;DR: In this article, the authors present a 2-parameter Generalized Exponential Distribution (GED) model and compare the performance of the estimators and compare them to the maximum likelihood estimators.
Abstract: In the beginning, we mention a historical recursion, a presentation of the
2-parameter Generalized exponential distribution ( distribution type, probability density function etc.) and we also mention basic characteristics of the distribution.
Basic definitions and theorems about point estimation and Bayes estimation are reported.
Furthermore, we discource on the analysis of the model and basic properties of the Generalized exponential distribution. Special themes, such as survival functions, Fisher information, order statistics, sum distribution and production of random numbers are analyzed in the frame of the Generalized exponential distribution.
Moreover, we analyze and apply point estimation methods (maximum likelihood, method of moments, percentile estimation, least (and weighted least) squares, method of L-moments) in order to estimate parameters of the distribution. Performance of the estimators for different estimation methods is also analyzed.
Next, bayesian estimation of the parameters (under squared error loss function and LINEX loss function) is coming up for discussion. We also analyze the performance of the estimators and compare them to the maximum likelihood estimators.
Finally, we present approximation of an actuarial table via Generalized exponential distribution.
1 citations
01 Jan 1984
TL;DR: In this article, the estimation of parameters of asymptotic distributions of extreme order statistics from exponential type parents is studied, and moment and maximum likelihood methods are compared relative to the latter for the top ten order statistics.
Abstract: This paper is concerned with the estimation of parameters of asymptotic distributions of extreme order statistics from exponential type parents. Moment and maximum likelihood methods are discussed; the asymptotic efficiency of the former method relative to the latter is evaluated for the top ten order statistics.
1 citations
TL;DR: In this article, the class of asymptotic distributions of the standardized Ψ-sums for a class of distributions is obtained on the basis of an extension for an early result of Khintchine.
Abstract: On the basis of an extension for an early result of Khintchine, the class of asymptotic distributions of the standardized Ψ-sums for a class of distributions is obtained in this paper.
1 citations