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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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Journal ArticleDOI
M. A. Beg1
01 Dec 1980-Metrika
TL;DR: In this paper, the Blackwell-Rao and Lehmann-Scheffe theorems are used to derive the minimum variance unbiased estimator for the two-parameter exponential distribution.
Abstract: In this paper the Blackwell-Rao and Lehmann-Scheffe theorems are used to derive the minimum variance unbiased estimator ofP=Pr{Y

40 citations

Journal ArticleDOI
TL;DR: In this paper, the robustness of T2 for samples of size 5, 10 and 20 from several bivariate distributions is investigated, including normal, uniform, exponential, gamma, lognormal and double exponential distributions.
Abstract: The robustness of T2 for samples of size 5, 10 and 20 from several bivariate distributions is investigated. Samples are presented from bivariate normal, uniform, exponential, gamma, lognormal and double exponential distributions. Related observations on the one sample t and paired t are also given. Highly skewed distributions resulted in too many extreme values of T2 Other distributions gave conservative results. The use of the t-test and non-simultaneous techniques gave large overall levels of significance.

40 citations

Journal ArticleDOI
TL;DR: In this paper, the authors used a mixture of exponentials distribution, namely the sum of exponential distributions characterized by the different eruption occurrence rates that may be recognized inspecting the cumulative number of eruptions with time in specific VEI (Volcanic Explosivity Index) categories.
Abstract: . The assessment of volcanic hazard is the first step for disaster mitigation. The distribution of repose periods between eruptions provides important information about the probability of new eruptions occurring within given time intervals. The quality of the probability estimate, i.e., of the hazard assessment, depends on the capacity of the chosen statistical model to describe the actual distribution of the repose times. In this work, we use a mixture of exponentials distribution, namely the sum of exponential distributions characterized by the different eruption occurrence rates that may be recognized inspecting the cumulative number of eruptions with time in specific VEI (Volcanic Explosivity Index) categories. The most striking property of an exponential mixture density is that the shape of the density function is flexible in a way similar to the frequently used Weibull distribution, matching long-tailed distributions and allowing clustering and time dependence of the eruption sequence, with distribution parameters that can be readily obtained from the observed occurrence rates. Thus, the mixture of exponentials turns out to be more precise and much easier to apply than the Weibull distribution. We recommended the use of a mixture of exponentials distribution when regimes with well-defined eruption rates can be identified in the cumulative series of events. As an example, we apply the mixture of exponential distributions to the repose-time sequences between explosive eruptions of the Colima and Popocatepetl volcanoes, Mexico, and compare the results obtained with the Weibull and other distributions.

40 citations

Journal ArticleDOI
TL;DR: In this paper, the distribution functions of 3, fj+ and 1- for the exponential case are derived from general results for order statistics, and computationally efficient approximations to these distribution functions are obtained.
Abstract: SUMMARY Let 1, b+ and 13- denote Kolmogorov-Smirnov type one-sample statistics to test goodness of fit in the presence of unknown nuisance parameters; then the distributions of b, fj+ and i- depend on the population sampled and the estimator used. Simulation has been the primary tool for studying these statistics. Recently, Durbin obtained the distributions of D1, + and b- in terms of a Fourier transform for a wide class of underlying populations, and produced explicit results for the exponential case. In this paper, the distribution functions of 3, fj+ and 1- for the exponential case are derived from general results for order statistics, and computationally efficient approximations to these distribution functions are obtained. In the course of this derivation, Bonferroni inequalities of Kounias, and Sobel & Uppuluri are generalized. Certain problems of goodness-of-fit testing in the presence of nuisance parameters, whose solutions make use of existing tables, are also discussed. These problems include the Pareto, Rayleigh, power function, and uniform distributions.

40 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202262
202114
202010
20196
201823