Journal ArticleDOI
Generalized Exponential Distributions
Rameshwar D. Gupta,Debasis Kundu +1 more
TLDR
In this article, a three-parameter generalized exponential distribution (GED) was used for analysis of lifetime data, which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar et al.Abstract:
Summary The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.read more
Citations
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Reliability Engineering and System Safety
TL;DR: In this paper, a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions is presented.
Journal ArticleDOI
Families of distributions arising from distributions of order statistics
TL;DR: In this article, a simple generalisation of the use of the collection of order statistic distributions associated with symmetric distributions is presented, and an alternative derivation of this family of distributions is as the result of applying the inverse probability integral transformation to the beta distribution.
Journal ArticleDOI
Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages
TL;DR: In this article, a two-parameter family of distributions on (0, 1) is explored, which has many similarities to the beta distribution and a number of advantages in terms of tractability.
Journal ArticleDOI
The beta exponential distribution
Saralees Nadarajah,Samuel Kotz +1 more
TL;DR: A comprehensive treatment of the mathematical properties of the beta exponential distribution generated from the logit of a beta random variable is provided and an expression for the Fisher information matrix is provided.
Journal ArticleDOI
The Weibull-G Family of Probability Distributions
TL;DR: The Weibull distribution is the most important distribution for problems in reliability as discussed by the authors, and it has been studied extensively in the literature, including in the context of the wider Weibbull-G family of distributions.
References
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Book
Continuous univariate distributions
TL;DR: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes
Journal ArticleDOI
Statistical Theory of Reliability and Life Testing Probability Models
Book
Statistical Models and Methods for Lifetime Data
TL;DR: Inference procedures for Log-Location-Scale Distributions as discussed by the authors have been used for estimating likelihood and estimating function methods. But they have not yet been applied to the estimation of likelihood.
Book
Statistical Theory of Reliability and Life Testing: Probability Models
Richard E. Barlow,Frank Proschan +1 more
TL;DR: A number of new classes of life distributions arising naturally in reliability models are treated systematically and each provides a realistic probabilistic description of a physical property occurring in the reliability context, thus permitting more realistic modeling of commonly occurring reliability situations.
Book
Modelling Extremal Events: for Insurance and Finance
TL;DR: In this article, an approach to Extremes via Point Processes is presented, and statistical methods for Extremal Events are presented. But the approach is limited to time series analysis for heavy-tailed processes.
Related Papers (5)
Exponentiated exponential family: an alternative to gamma and weibull distributions
Rameshwar D. Gupta,Debasis Kundu +1 more
Exponentiated Weibull family for analyzing bathtub failure-rate data
G.S. Mudholkar,D.K. Srivastava +1 more