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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2 citations
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TL;DR: In this paper, a simple moment-based procedure for testing homogeneity in the natural exponential family with quadratic variance functions is proposed, which directly tests the hypotheses without the need to establish parameter estimability.
2 citations
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TL;DR: In this article, a new family of distribution considering Generalized Marshal-Olkin distribution as the base line distribution in the Beta-G family of construction is proposed, which includes Beta G (Eugene et al. 2002 and Jones, 2004) and Jayakumar and Mathew, 2008) families as particular cases.
Abstract: In this paper we propose a new family of distribution considering Generalized Marshal-Olkin distribution as the base line distribution in the Beta-G family of Construction. The new family includes Beta-G (Eugene et al. 2002 and Jones, 2004) and (Jayakumar and Mathew, 2008) families as particular cases. Probability density function (pdf) and the cumulative distribution function (cdf) are expressed as mixture of the Marshal-Olkin (Marshal and Olkin, 1997) distribution. Series expansions of pdf of the order statistics are also obtained. Moments, moment generating function, Renyi entropies, quantile power series, random sample generation and asymptotes are also investigated. Parameter estimation by method of maximum likelihood and method of moment are also presented. Finally proposed model is compared to the Generalized Marshall-Olkin Kumaraswamy extended family (Handique and Chakraborty, 2015) by considering three data fitting examples with real life data sets.
2 citations
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TL;DR: In this paper, it was shown that the modified power series distribution (MPSD) and the Lagrange probability distribution (LPD) represent the same probability model and a theorem on the MVU estimation of a function (θ) of the parameter θ in the LPSD is stated with the necessary conditions.
Abstract: It is shown that the modified power series distribution (MPSD) [GUPTA, 1974] the Lagrange probability distribution (LPD) [CONSUL SHENTON, 1972, the LAGBANGE power series distribution (LPSD) [JAIN, 1975] and the discrete exponential family (DEE) distribution [JANARDAN, 1982) represent the same probability model. A theorem on the MVU estimation of a function (θ) of the parameter θ in the LPSD is stated with the necessary conditions. The theorem is then applied to derive the MVU estimators for the mean, square of the mean and the variance of the generalized POISSON .distribution, generalized negative binomial distribution and some other related distributions
2 citations