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: In this paper, a comparative study of two-parameter gamma and Weibull distributions for modeling lifetime data from various fields of knowledge is presented, where the authors compare the goodness of fit of the two distributions for lifetime data.
Abstract: The analysis and modeling of lifetime data are crucial in almost all applied sciences including medicine, insurance, engineering, behavioral sciences and finance, amongst others. The main objective of this paper is to have a comparative study of two-parameter gamma and Weibull distributions for modeling lifetime data from various fields of knowledge. Since exponential distribution is a particular case of both gamma and Weibull distributions and the exponential distribution is a classical distribution for modeling lifetime data, the goodness of fit of both gamma and Weibull distributions are compared with exponential distribution.
13 citations
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13 citations
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01 Dec 2015TL;DR: In this paper, a modified Weibull geometric distribution (MWEG) was introduced, which is a new class of lifetime distributions by compounding the modified Weigull and geometric distributions.
Abstract: A new class of lifetime distributions is introduced by compounding the modified Weibull and geometric distributions, the so-called modified Weibull geometric distribution. It includes as special submodels such as linear failure rate geometric distribution, Weibull geometric distribution, exponential geometric distribution, among others. We study its structural properties including probability density function, hazard functions, moments, generating and quantile functions. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. Estimation by maximum likelihood and inference for a large sample are presented. An expectation-maximization algorithm is used to determine the maximum likelihood estimates of the parameters. Finally, a real data set is analyzed for illustrative purposes.
13 citations
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TL;DR: Asymptotically best linear unbiased estimators (ABLUE) of quantiles, x^., in the two-parameter (location-scale) exponential and double exponential families are obtained as linear combinations of two suitably chosen order statistics as discussed by the authors.
Abstract: Asymptotically best linear unbiased estimators (ABLUE) of quantiles, x^., in the two-parameter (location-scale) exponential and double exponential families are obtained as linear combinations of two suitably chosen order statistics. Exact formulae for the linear combinations are given as functions of £. The derived estimators in both cases compare favorably with the usual nonparametric estimator. Also, in the exponential case the derived estimator compares favorably with the Sarhan-Greenberg BLUE based on a complete sample
13 citations
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TL;DR: In this article, the authors modified the bootstrap predictive distribution by replacing the maximum likelihood estimator of the unknown parameter by its minimum Hellinger distance estimator, which is asymptotically superior to the corresponding estimative distribution in terms of the average Kullback-Leibler divergence.
Abstract: SUMMARY The bootstrap predictive distribution considered by Harris (1989) is modified by replacing the maximum likelihood estimator of the unknown parameter by its minimum Hellinger distance estimator. The predictive distribution thus obtained is asymptotically superior to the corresponding estimative distribution in terms of the average Kullback-Leibler divergence, when the true distribution is in the natural exponential family. Simulation results are provided for the binomial and normal distributions which suggest that the proposed predictive distributions are robust and can perform better than the likelihood based methods under data contamination.
13 citations