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 2004
TL;DR: In this article, the authors proposed a non-linear exponential (NLINEX) loss function, which is quite asymmetric in nature and obtained the Bayes estimator under exponential(LINEX) and squared error(SE) loss functions.
Abstract: In this paper we have proposed a new loss function, namely, non-linear exponential(NLINEX) loss function, which is quite asymmetric in nature. We obtained the Bayes estimator under exponential(LINEX) and squared error(SE) loss functions. Moreover, a numerical comparison among the Bayes estimators of power function distribution under SE, LINEX, and NLINEX loss function have been made.
7 citations
TL;DR: In this article, it was shown that the limiting law F 0 of Y t − t as t → 0 is a Pareto type law with the form F 0 ( u ) = 0 for u 1 and the form 1 − u − l for u ≥ 1.
7 citations
Journal Article•
TL;DR: The generalized Weibull-exponential distribution (GWED) as discussed by the authors is a new distribution that extends the Weibell-expansion distribution with additional properties such as moments, limiting behavior, quantile function, Shannon entropy, skewness and kurtosis.
Abstract: This paper defines a new distribution, namely, Generalized Weibull- Exponential distribution GWED. This distribution extends a Weibull-Exponential distribution which is generated from family of generalized T-X distributions. Different properties for the GWED are obtained such as moments, limiting behavior, quantile function, Shannon’s entropy, skewness and kurtosis. Finally, analysis of several real data sets are carried out and thereafter compared the results with other distributions to illustrate the applications of the GWED.
7 citations
TL;DR: In this article, the robust estimation of parameters of exponential and double exponential distributions in the presence of multiple outliers is discussed. But the results are restricted to the case of a single outlier.
Abstract: Publisher Summary This chapter discusses the robust estimation of parameters of exponential and double exponential distributions in the presence of multiple outliers. It provides an alternative, more direct proof of the above recursion algorithm and to extend the numerical results to include larger sample sizes and also to accomodate a larger number of outliers. It considers generalizations of the Chikkagoudar–Kunchur estimator discussed by Balakrishnan and Barnett, provides a further generalization, and extends these results to include larger sample sizes and more outliers. The moments of order statistics from the multiple-outlier exponential model and some equations relating them are used in the moments of order statistics from the multiple-outlier double exponential model to examine the robustness properties of various linear estimators of the location and scale parameters of the double exponential (Laplace) distribution in the presence of one or more outliers. These results generalize those obtained by Balakrishnan and Ambagaspitiya, who examined the case of a single outlier.
7 citations
TL;DR: In this paper, the authors considered the probability distribution of the volume of a certain substance (e.g., river discharge, rainfall, deposites of clay, organism, etc.) that flows into a semi-infinite reservoir before its first emptiness for continuous and homogeneous input process when the substance is released at unit rate per unit of time.
Abstract: This paper considers the probability distribution of the volume of a certain substance (e.g. river discharge, rainfall, deposites of clay, organism, etc.) that flows into a semi-infinite reservoir before its first emptiness for continuous and homogeneous input process when the substance is released at unit rate per unit of time. A few moments of the distribution have been computed. A generalized gamma, and a generalized exponential distributions as particular cases are also discussed. Some possible applications of the generalized negative exponential distribution have been mentioned. These distributions are in fact the continuous analogues of the discrete LAGRANGE distributions recently considered by JAIN and others.
7 citations