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
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The extended power distribution: A new distribution on $(0, 1)$
TL;DR: In this article, a two-parameter bounded probability distribution called the extended power distribution is proposed, which is similar to the beta distribution but has some advantages over the Kumaraswamy and beta distributions.
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TL;DR: Martinez-Florez et al. as discussed by the authors defined two new probability distributions, unibimodal symmetric model with proportional hazard function to the normal distribution and uni-modal asymmetric model to the skew normal distribution.
Proceedings ArticleDOI
Two-sided Topp-Leone Weibull distribution
TL;DR: In this article, a two-sided Topp-Leone generated Weibull distribution has been proposed and its quantile function has been presented in several shapes of distributions such as decreasing, unimodal, and bimodal.
A Generalized Logistic Distribution
TL;DR: In this paper, a complete study of the transmuted Kumaraswamy Logistic distribution is proposed, introducing some basic properties of this distribution, such as quantile function, characteristic function and entropy, as well as the derivation of maximum likelihood estimates of the parameters and the 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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