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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01 Jan 1985
1 citations
01 Jan 2013
TL;DR: The exponential distribution is one of the major bricks in many models in operations research in general and in queueing theory in particular as mentioned in this paper, however, this is not always the case and, as we will see throughout the book, more involved treatment is needed in cases where the assumption of an exponential distribution needs to be removed.
Abstract: The exponential distribution is one of the major bricks in many models in operations research in general and in queueing theory in particular. Exponential random variables possess convenient properties, especially the memoryless property which makes the analysis of such models tractable. Also, they are simple to deal with as they are a single parameter family of distributions. At the same time, these distributions are a good model for representing real-life situations (such as interarrival times to a queueing system). Yet, this is not always the case and, as we will see throughout the book, more involved treatment is needed in cases where the assumption of an exponential distribution needs to be removed.
1 citations
TL;DR: In this article, the scale parameter of the exponential distribution for Type I, Type II, and randomly censored data are derived and the inferences concerning the two-parameter exponential distribution are also considered.
Abstract: Publisher Summary This chapter discusses the properties of order statistics and uses the results for estimating the parameters of the one and two parameter exponential distributions. It summarizes the important properties of order statistics from the exponential distribution and describes various types of censoring. The estimates of scale parameter of the exponential distribution for Type I, Type II, and randomly censored data are derived in the chapter. The inferences concerning the two-parameter exponential distribution are also considered in the chapter. These results are extended to two or more independent Type II censored samples. Order restricted inference for the scale parameters of exponential distributions are also discussed in the chapter. Bayesian inference and Bayesian estimates of scale parameter, for Type I and Type H censored samples, are presented in the chapter.
1 citations
TL;DR: In this article, the Morris family of six distributions were characterized as the only distributions among the standard exponential families whose orthogonal projection of the sample variance in a proper estimating function space, is a quadratic polynomial of the sampled mean.
Abstract: The aim of this paper is to characterize the Morris family of six distributions as the only distributions among the standard exponential families whose orthogonal projection of the sample variance in a proper estimating function space, is a quadratic polynomial of the sample mean. The above family is also characterized by sufficiency in estimating functions spaces.
1 citations
TL;DR: For a given square matrix A, the numerical range for the exponential function e^(At), t in C, is considered in this article, where geometrical and topological properties of numerical range are presented.
Abstract: For a given square matrix A, the numerical range for the exponential function e^(At), t in C, is considered. Some geometrical and topological properties of the numerical range are presented.
1 citations