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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TL;DR: The exponential distribution is considered in situtations where intervals between events are considered as well as where a skewed distribution is appropriate as mentioned in this paper, and the exponential distribution also plays key role in survival analysis.
Abstract: The exponential distribution is considered in situtations where intervals between events are considered as well as where a skewed distribution is appropriate. The exponential distribution also plays key role in survival analysis. Goodness-of-fit for exponentiality is crucial as, in the natural sciences, some of the commonly used distributions such as gamma and Weibull distributions are just translated versions of the exponential distributions. Several well known exponentiality tests are reviewed. A power comparison is performed using simulation.
3 citations
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TL;DR: In this article, the reliability analysis for the two-parameter exponential distribution on the basis of the life tests that are terminated after a pre assigned number of failures, when the prior distribution of the location parameter, given the scale, is assumed to be exponential, while the scale parameter has an inverse Gaussian prior distribution, is discussed.
Abstract: This paper discusses the Bayesian reliability analysis for the two-parameter exponential distribution on the basis of the life tests that are terminated after a pre assigned number of failures, when the prior distribution of the location parameter, given the scale, is assumed to be exponential, while the scale parameter is assumed to have an inverse Gaussian prior distribution. The usual assumption of the squared error loss function is also made. A situation dealing with attribute life testing is also considered.
3 citations
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3 citations
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3 citations
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TL;DR: The null distribution of the likelihood ratio criterion for testing the quality of scale parameters of p(p>2) two parameter exponential distributions for the case of equal sample sizes is obtained in a closed form for the first time as discussed by the authors.
Abstract: In this paper, null distribution of the likelihood ratio criterion for testing the quality of scale parameters of p(p>2) two parameter exponential distributions for the case of equal sample sizes is obtained in a closed form for the first time. A short table of the critical values of the test statistic is also presented.
3 citations