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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 results show that it is possible to combine these two methods to compute exponential divided differences accurately, and a hybrid algorithm is presented for which the error bound grows quite slowly with the order of the divided difference.
Abstract: : The traditional recurrence for the computation of exponential divided differences, along with a new method based on the properties of the exponential function, are studied in detail in this paper. Our results show that it is possible to combine these two methods to compute exponential divided differences accurately. A hybrid algorithm is presented for which our error bound grows quite slowly with the order of the divided difference. (Author)

33 citations

Journal ArticleDOI
TL;DR: In this paper, the density of the beta Weibull distribution is expressed as a mixture of Weibbull densities and two closed-form expressions are derived for their moments.
Abstract: In this paper, we study some mathematical properties of the beta Weibull (BW) distribution, which is a quite flexible model in analysing positive data. It contains the Weibull, exponentiated exponential, exponentiated Weibull and beta exponential distributions as special sub-models. We demonstrate that the BW density can be expressed as a mixture of Weibull densities. We provide their moments and two closed-form expressions for their moment-generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and two entropies. The density of the BW-order statistics is a mixture of Weibull densities and two closed-form expressions are derived for their moments. The estimation of the parameters is approached by two methods: moments and maximum likelihood. We compare the performances of the estimates obtained from both the methods by simulation. The expected information matrix is derived. For th...

33 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202262
202114
202010
20196
201823