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.

Sequential estimation of a restricted mean parameter of an exponential family

Abstract: The estimation of restricted parameters by fixed sample size rules has been considered by Hammersley [1]. A sequential solution to the problem of estimating the mean of a normal distribution when it is some unknown integer and a general method for solving problems of this sort were studied by Robbins in [4]. Based on the work of Robbins, a sequential procedure for estimating the parameter of a Poisson distribution when it is known to be an integer was given in [3]. The results obtained herein represent a generalization of the work dealing with the normal and Poisson cases. A class of sequential procedures is proposed and bounds on the error probabilities are obtained. The expected sample sizes are investigated and a weak form of optimality is demonstrated under certain conditions.

The Bivariate Order Statistics for Exponential Distribution

Abstract: In this paper we have derived the distribution of bivariate order statistics and joint distribution of two bivariate order statistics for standard exponential distribution. The moments of proposed distributions have also been derived.

On the Representation of Correlated Exponential Distributions by Phase Type Distributions

Abstract: In this paper we present results for bivariate exponential distributions which are represented by phase type distributions. The paper extends results from previous publications [3, 11] on this topic by introducing new representations that require a smaller number of phases to reach some correlation coefficient and introduces different ways to describe correlation between exponentially distributed random variables.