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 new class of exponential sums from which various known as well as new exponential sums are generated is introduced, and a class of generalized Poisson distributions is defined (GPDs).
Abstract: In these paper we introduce a new class of exponential sums from which various known as well as new exponential sums are generated. Then a class of generalized Poisson distributions is defined (GPDs). Some well known and new distributions are obtained from GPDs. Some recurrence relations of the parameters of these distributions is studied. The suitability of these distributions is illustrated through some real life data.
7 citations
7 citations
TL;DR: In this paper, a new class of positive infinitely divisible probability laws called 𝔏γ distributions were introduced and their cumulant generating functions were expressed in terms of the principal branch of the Lambert W function.
Abstract: We introduce a new class of positive infinitely divisible probability laws calling them 𝔏γ distributions. Their cumulant-generating functions (cgf) are expressed in terms of the principal branch of the Lambert W function. The probability density functions (pdfs) of 𝔏γ laws are bounded resembling pdf of a Levy stable distribution. The exponential dispersion model constructed starting from an 𝔏γ distribution admits the inverse Gaussian approximation. The natural exponential family constructed starting from an 𝔏γ distribution constitutes the reciprocal of the natural exponential family generated by a spectrally negative stable law with α = 1. We derive new results on 𝔏γ laws and the related exponential dispersion models, including their convolution and scaling closure properties. We generate another exponential dispersion model starting from an exponentially compounded 𝔏γ law. This distribution emerges in the Poisson mixture representation of a generalized Poisson law. We extend the Poisson approximation for...
7 citations
TL;DR: In this article, the problem of approximating a prior by a suitable finite mixture of distributions, with respect to Prokhorov's metric, is considered and the error of approximation when the statistical model is a suitable exponential family is given.
7 citations
TL;DR: In this paper, a Cacoullos-type lower bound for the variance of a random vector X belonging to the multidimensional exponential family is given, which is shown to characterize the exponential family.
7 citations