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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
TL;DR: In this article, a new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two-parameter extension of the exponential distribution which may serve as a competitor to such commonly-used twoparameter families of life distributions as the Weibull, gamma and lognormal distributions.
Abstract: SUMMARY A new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two-parameter extension of the exponential distribution which may serve as a competitor to such commonly-used two-parameter families of life distributions as the Weibull, gamma and lognormal distributions. In addition, the general method is applied to yield a new three-parameter Weibull distribution. Families expanded using the method introduced here have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution again in the family. Bivariate versions are also considered.

1,016 citations

Journal ArticleDOI
Roger Ratcliff1
TL;DR: It is shown that this method of averaging is exact for certain distributions (i.e., the resulting distribution belongs to the same family as the individual distributions) and Monte Carlo studies and application of the method provide evidence that properties derived from the group reaction time distribution are much the same as average propertiesderived from the data of individual subjects.
Abstract: A method of obtaining an average reaction time distribution for a group of subjects is described. The method is particularly useful for cases in which data from many subjects are available but there are only 10-20 reaction time observations per subject cell. Essentially, reaction times for each subject are organized in ascending order, and quantiles are calculated. The quantiles are then averaged over subjects to give group quantiles (cf. Vincent learning curves). From the group quantiles, a group reaction time distribution can be constructed. It is shown that this method of averaging is exact for certain distributions (i.e., the resulting distribution belongs to the same family as the individual distributions). Furthermore, Monte Carlo studies and application of the method to the combined data from three large experiments provide evidence that properties derived from the group reaction time distribution are much the same as average properties derived from the data of individual subjects. This article also examines how to quantitatively describe the shape of reaction time distributions. The use of moments and cumulants as sources of information about distribution shape is evaluated and rejected because of extreme dependence on long, outlier reaction times. As an alternative, the use of explicit distribution functions as approximations to reaction time distributions is considered.

971 citations

Journal ArticleDOI
TL;DR: In this paper, a new family of generalized distributions for double-bounded random processes with hydrological applications is described, including Kw-normal, Kw-Weibull and Kw-Gamma distributions.
Abstract: Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79–88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix ‘Kw’) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with a...

742 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed two general fading distributions, the kappa-mu distribution and the eta-mu distributions, for line-of-sight applications, for which fading models are proposed.
Abstract: This paper presents two general fading distributions, the kappa-mu distribution and the eta-mu distribution, for which fading models are proposed. These distributions are fully characterized in terms of measurable physical parameters. The kappa-mu distribution includes the Rice (Nakagami-n), the Nakagami-m, the Rayleigh, and the one-sided Gaussian distributions as special cases. The eta-mu distribution includes the Hoyt (Nakagami-q), the Nakagami-m, the Rayleigh, and the one-sided Gaussian distributions as special cases. Field measurement campaigns were used to validate these distributions. It was observed that their fit to experimental data outperformed that provided by the widely known fading distributions, such as the Rayleigh, Rice, and Nakagami-m. In particular, the kappa-mu distribution is better suited for line-of-sight applications, whereas the eta-mu distribution gives better results for non-line-of-sight applications.

728 citations

Book
05 May 2014
TL;DR: In this article, the information and exponential families in statistical theory were studied. But they did not consider the exponential family in the context of exponential families. And they were not considered in this paper.
Abstract: (1980). Information and Exponential Families in Statistical Theory. Technometrics: Vol. 22, No. 2, pp. 280-280.

717 citations


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