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.
Papers published on a yearly basis
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TL;DR: In this article, the problem of selecting the particular process with the larger mean life is considered, and three techniques are considered and three procedures are constructed to show their advantages, and an alternative sequential procedure has also been proposed and shown to be valuable in some situations.
Abstract: Given two production processes, the units from which fail in accordance with the Weibull distribution, the problem of selecting the particular process with the larger mean life is considered. Three techniques are considered and three procedures are constructed to show their advantages. An alternative sequential procedure has also been proposed and shown to be valuable in some situations. This paper may be regarded as a generalization of Sobel's earlier work [21] on the exponential distribution.
16 citations
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TL;DR: In this article, two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property, motivated by the notion of relevance of distributions introduced by Krakowski (1973).
Abstract: : In this note two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property. These results were motivated by the notion of 'relevation of distributions' introduced by Krakowski (1973). (Author)
16 citations
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16 citations
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TL;DR: The generalized exponential function is proposed to approximate the underlying Weibull or Gamma distributions, and then solves for the RF using Laplace transform.
Abstract: When the inter-renewal time follows the Weibull or the Gamma distribution, the analytical renewal function (RF) usually is not tractable, and approximation method has been used. Instead of approximating RF directly, this article proposes the generalized exponential function to approximate the underlying Weibull or Gamma distributions, and then solves for the RF using Laplace transform. Parameters for generalized exponential function can be obtained by solving a simple optimization problem. The method can obtain accurate RF approximations where the inter-renewals follow Weibull or Gamma distributions, yet analytical RF is still desirable. Comprehensive analysis shows that the new model is mathematically accurate and computationally convenient to approximate the Weibull RF given its shape parameter β ∈ [1, 5]. For the Gamma distribution, the proposed model can achieve good approximations when the Gamma shape parameter k ∈ [1, 10]. These are the typical ranges of shape parameters when modeling the product re...
15 citations
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TL;DR: The pairwise-only dependence assumption is relaxed, and the necessary form that one-parameter exponential family conditional densities must take under more general conditions of multiway dependence is given.
15 citations