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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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TL;DR: The directional precision of the sample mean estimator was calculated analytically for the offset exponential and normal distributions in three-dimensional space both for a finite sample and for limiting cases as discussed by the authors.
Abstract: The directional precision of the sample mean estimator was calculated analytically for the offset exponential and normal distributions in three-dimensional space both for a finite sample and for limiting cases. It was shown that the spherical projection of the sample mean of the shifted exponential distribution has connections with modified Bessel functions and with hypergeometric functions. It was shown explicitly how the distribution of the sample mean of the exponential pdf converges near the mode to the normal distribution. Approximation formulae for the distribution of the sample mean of the shifted exponential distribution and for its directional precision and for the precision of the estimation of the direction of shift of the normal distribution were obtained.
1 citations
31 Oct 2011
TL;DR: In this article, the results established by Joshi in [4] and [5] for order statistics from the standard exponential distribution were extended here for the case of doubly truncated generalized exponential distribution.
Abstract: In this article, the results established by Joshi in [4] and [5] for order statistics from the standard exponential distribution and the results established by Saran and Pushkarna in [10] for order statistics from generalized exponential distribution are extended here for the case of doubly truncated generalized exponential distribution. In addition, percentage points are derived; simulation results for the single and product moments of order statistics are obtained. Keywords: Generalized exponential distribution, order statistics, single moments, product moments, and truncation.
1 citations
TL;DR: In this paper, the existence of the maximum likelihood estimate (MLE) of the parameter for 1-dimensional exponential families was investigated and it was established that the MLE exists in most cases.
1 citations
01 Jan 1997
TL;DR: In this article, a necessary condition for the existence of any weakly consistent estimator is presented in exponential family nonlinear models and one more necessary condition is given for a consistent estimators in generalized linear models.
Abstract: In this paper, a necessary condition for the existence of any weakly consistentestimator is presented in exponential family nonlinear models. Then we give one morenecessary condition for a consistent estimator in generalized linear models. Under mildregularity conditions, the existence, the strong consistency and the asymptotic normalityof MLE are proved in exponential family nonlinear models. Our results may be regardedas a further work of [1] in generalized linear models.
1 citations
16 Jun 2014
TL;DR: In this paper, a numerical experiment was performed using a shooting and bouncing ray based solver on eight finite clusters of eight perfectly electrically conductive canonical target geometries where each finite cluster volume includes certain amount of randomly translated and rotated target of one kind.
Abstract: A numerical experiment is performed using a Shooting and Bouncing Rays based solver on eight finite clusters of eight perfectly electrically conductive canonical target geometries where each finite cluster volume includes certain amount of randomly translated and rotated target of one kind. The best probability density function that best fits to the obtained mono-static radar cross section distribution is investigated among exponential, gamma, Weibull, and log-normal distributions. Numerical results show how probability density functions for considered targets with fluctuating radar cross sections deviate from Swerling-Weibull models especially from a point of view considering the stealth measures in target designs.
1 citations