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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01 Jan 1984
TL;DR: In this article, it was shown that there are exactly min(n+1, m) different positive values of γ with this property, where m is the number of positive values γ.
Abstract: Let Rn/m(z, γ)=Pn(z; γ)/(1-γz)m be a restricted rational approximation to exp(z), zeℂ, of order n for all real γ. In this paper we discuss how γ can be used to obtain fitting at a real non-positive point z1. It is shown that there are exactly min(n+1, m) different positive values of γ with this property.
6 citations
5 citations
TL;DR: In this article, it was shown that the Maxwell-Boltzmann distribution (exponential distribution) is the continuum limit of Bose-Einstein statistics, which is the same as the limit of the exponential distribution.
5 citations
5 citations
TL;DR: In this article, a rational Laplace-Stieltjes transform with a pole of maximal real part is used to determine whether or not the numerator polynomial admits a transform that corresponds to a matrix exponential distribution.
Abstract: A necessary condition for a rational Laplace–Stieltjes transform to correspond to a matrix exponential distribution is that the pole of maximal real part is real and negative. Given a rational Laplace–Stieltjes transform with such a pole, we present a method to determine whether or not the numerator polynomial admits a transform that corresponds to a matrix exponential distribution. The method relies on the minimization of a continuous function of one variable over the nonnegative real numbers. Using this approach, we give an alternative characterization for all matrix exponential distributions of order three.
5 citations