Journal ArticleDOI
The Exponentiated Type Distributions
Saralees Nadarajah,Samuel Kotz +1 more
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TLDR
In this paper, the authors introduced four more exponentiated type distributions that generalize the standard gamma, standard Weibull, standard Gumbel and the standard Frechet distributions in the same way the exponentiated exponential distribution generalizes the standard exponential distribution.Abstract:
Gupta et al. [Commun. Stat., Theory Methods 27, 887–904, 1998] introduced the exponentiated exponential distribution as a generalization of the standard exponential distribution. In this paper, we introduce four more exponentiated type distributions that generalize the standard gamma, standard Weibull, standard Gumbel and the standard Frechet distributions in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. A treatment of the mathematical properties is provided for each distribution.read more
Citations
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Journal ArticleDOI
The beta generalized exponential distribution
TL;DR: In this paper, a new distribution called the beta generalized exponential distribution is proposed, which includes the beta exponential and generalized exponential distributions as special cases, and the density function can be expressed as a mixture of generalized exponential densities.
Journal ArticleDOI
The Exponentiated Generalized Class of Distributions
TL;DR: In this article, a new method of adding two parameters to a continous distribution that extends the idea first introduced by Lehmann (1953) and studied by Nadarajah and Kotz (2006) is proposed.
Journal ArticleDOI
An extended Lindley distribution
TL;DR: In this article, an extension of the Lindley distribution for lifetime data is proposed. But the authors focus on the failure rate of lifetime data and do not consider the residual lifetime of the data.
Journal ArticleDOI
A new lifetime distribution
TL;DR: In this article, a new three-parameter distribution motivated mainly by lifetime issues is introduced, and a real data application is described to show its superior performance versus at least that of 15 of the known lifetime models.
Journal ArticleDOI
A generalization of the exponential-Poisson distribution
TL;DR: In this article, the authors generalize the exponential-Poisson (EP) distribution and show that the failure rate of the new distribution can be decreasing or increasing, and provide closed-form expressions for the density, cumulative distribution, survival and failure rate functions; they also obtain the density of the i th order statistic.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
A table of integrals
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions
Journal ArticleDOI
Integrals and Series
TL;DR: The pages of this expensive but invaluable reference work are dense with formulae of stupefying complexity as discussed by the authors, where definite/indefinite integral properties of a great variety of special functions are discussed.
Book
Extreme Value Distributions: Theory and Applications
Samuel Kotz,Saralees Nadarajah +1 more
TL;DR: Univariate extreme value distributions (UVD) as discussed by the authors, generalized extreme value distribution (GVD) and multivariate Extreme Value Distribution (MVDD) have been used to estimate the EVD.
Journal ArticleDOI
Exponentiated exponential family: an alternative to gamma and weibull distributions
Rameshwar D. Gupta,Debasis Kundu +1 more
TL;DR: In this paper, the authors studied the properties of a new family of distributions known as the Exponentiated Exponential (exponential) distribution, discussed in Gupta, Gupta, and Gupta (1998).
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