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 article, a new family of circular distributions, obtained by wrapping discrete skew Laplace distribution on Z = 0, ± 1, ± 2, around a unit circle, is presented.
Abstract: In this paper we propose a new family of circular distributions, obtained by wrapping discrete skew Laplace distribution on Z = 0, ±1, ±2, around a unit circle. In contrast with many wrapped distributions, here closed form expressions exist for the probability density function, the distribution function and the characteristic function. The properties of this new family of distribution are studied.
9 citations
TL;DR: In this article, a moment identity applicable to a general class of discrete probability distributions was derived for modified power series, Ord and Katz families, which has potential applications in different fields.
Abstract: In this paper, we obtain a moment identity applicable to a general class of discrete probability distributions. We then derive the corresponding identities for modified power series, Ord and Katz families. It is noted that the proposed identity has potential applications in different fields.
9 citations
TL;DR: In this paper, the normal inverse Gaussian distributions are used to introduce the class of multivariate normal α-stable distributions, and the expression of the variance function of the generated natural exponential family is given.
Abstract: The normal inverse Gaussian distributions are used to introduce the class of multivariate normal α-stable distributions. Some fundamental properties of these new distributions are established. We give the expression of the variance function of the generated natural exponential family and we use the Levy–Khintchine representation to determine the associated Levy measure. We also study the relationship between these distributions and the multivariate inverse Gaussian ones.
9 citations
TL;DR: In this paper, the modified slashed Rayleigh distribution (SRLD) is proposed and studied. But the proposed SRLD is an extension of the ordinary Rayleigh distributions, being more flexible in terms of distributional kurtosis, and it arises as a quotient of two independent random variables.
Abstract: A new family of slash distributions, the modified slashed-Rayleigh distribution, is proposed and studied. This family is an extension of the ordinary Rayleigh distribution, being more flexible in terms of distributional kurtosis. It arises as a quotient of two independent random variables, one being a Rayleigh distribution in the numerator and the other a power of the exponential distribution in denominator. We present properties of the proposed family. In addition, we carry out estimation of the model parameters by moment and maximum likelihood methods. Finally, we conduct a small-scale simulation study to evaluate the performance of the maximum likelihood estimators and apply the results to a real data set, revealing its good performance.
9 citations
TL;DR: A large number of characterizations of univariate exponential distributions are known; these often lead to a functional equation, relatively few of which have been extended to the multivariate case as discussed by the authors.
9 citations