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 2016
TL;DR: A sufficient statistic is a function of the observed data X containing all the information that X holds about the model as mentioned in this paper, and according to Rao-Blackwell-, Lehmann-Scheffe-theorems, statistical inference procedures must be based on such statistics for purposes of efficiency or optimality.
Abstract: A sufficient statistic is a function of the observed data X containing all the information that X holds about the model. A complete sufficient statistic is one that reduces the data the most, without losing any information. More importantly, according to Rao–Blackwell-, Lehmann–Scheffe-theorems, statistical inference procedures must be based on such statistics for purposes of efficiency or optimality.
TL;DR: In this paper, a new non-ruin measure associated with the aggregate logarithm of the claim-over-profit ratios was defined and obtained on Pareto-type distributions.
Abstract: In the general risk model (or the Sparre-Andersen model), it is well-known that the following assertion holds: if the claim size is exponentially distributed then the non-ruin probability distribution is a mixture of exponential distributions. In this paper, under some general conditions, we prove that the converse statement of the previous assertion is also true. Besides, we define a new non-ruin measure associated with the aggregate logarithms of the claim-over-profit ratios and obtain a result on Pareto-type distributions.
TL;DR: Some recurrence relations of single and product moments for order statistics from doubly truncated generalized exponential distribution are established and the recurrence relation of single moments is used to characterize the generalizedonential distribution.
Abstract: In this article, some recurrence relations of single and product moments for order statistics from doubly truncated generalized exponential distribution are establish we use the recurrence relation of single moments to characterize the generalized exponential distribution Keywords: Generalized exponential distribution, order statistics, single moments, product moments, truncation, characterization. AMS Classification: 2000 Mathematics Subject Classification: 62G30
TL;DR: In this paper, the acceptance-rejection algorithm is slow to simulate from mixture distributions when the acceptance probability is small, and reformulation as a mixture of general Erlang distributions may increase efficiency.
Abstract: The acceptance—rejection algorithm is slow to simulate from mixture distributions when the acceptance probability is small. For a mixture of exponential distributions, reformulation as a mixture of general Erlang distributions may increase efficiency. The reformulation which maximises acceptance probability can be found by linear programming. An example is given in which reformulation reduces the average simulation time by a factor of 15.
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TL;DR: In this paper, a Farlie-Gumbel-Morgenstern (FGM) family of bivariate linear exponential distributions generated from given marginal's is proposed, where properties of FGM are analogous to properties of Bivariate distributions.
Abstract: In this paper we propose a Farlie-Gumbel-Morgenstern (FGM) family of bivariate linear exponential distributions generated from given marginal's. Therefore, properties of FGM are analogous to properties of bivariate distributions. We study some important statistical properties and results for the new distribution.