Journal ArticleDOI
A new family of generalized distributions
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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...read more
Citations
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The Complementary Generalized Transmuted Poisson-G Family of Distributions
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Sine Topp-Leone-G family of distributions: Theory and applications
TL;DR: The sine TL-G family as discussed by the authors is a trigonometric family of distributions defined from the alliance of the families known as sine-G and Topp-Leone generated (TL-G).
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The odd log–logistic normal distribution: Theory and applications in analysis of experiments
TL;DR: In this paper, the odd log-logistic normal (OLLN) distribution is proposed, which is symmetric, platykurtic, leptokurtic and may be unimodal or bimodal.
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The McDonald Normal Distribution
TL;DR: In this paper, a five-parameter distribution called the McDonald normal distribution is defined and studied, which contains several important distributions discussed in the literature, such as the normal, skew-normal, exponentiated normal, beta normal and Kumaraswamy normal distributions, among others.
Journal ArticleDOI
The Kumaraswamy GP Distribution
TL;DR: The authors proposed a tractable generalization of the generalized Pareto (GP) distribution for extreme values, which is the most popular model for extreme value modeling and provides a comprehensive treatment of mathematical properties, estimate parameters by the method of maximum likelihood and provide the observed information matrix.
References
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Journal ArticleDOI
Statistical Theory of Reliability and Life Testing Probability Models
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.
Journal ArticleDOI
L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics
TL;DR: The authors define L-moments as the expectations of certain linear combinations of order statistics, which can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions.
Journal Article
A class of distributions which includes the normal ones
TL;DR: In this paper, a nouvelle classe de fonctions de densite dependant du parametre de forme λ, telles que λ=0 corresponde a la densite normale standard.
Journal ArticleDOI
Generalized additive models for location, scale and shape
TL;DR: The generalized additive model for location, scale and shape (GAMLSS) as mentioned in this paper is a general class of statistical models for a univariate response variable, which assumes independent observations of the response variable y given the parameters, the explanatory variables and the values of the random effects.
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