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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Journal ArticleDOI
A better approach to discuss medical science and engineering data with a modified Lehmann Type – II model
TL;DR: A modified Lehmann type II (ML-II) model was discussed as a better approach to modeling bathtub-shaped and asymmetric random phenomena and demonstrated ML- II's dominance over well-known competitors by modeling anxiety in women and electronic data.
Journal ArticleDOI
Transmuted Kumaraswamy-G Family of Distributions for Modelling Reliability Data
TL;DR: In this paper, the authors introduced a new class of distributions, called the transmuted Kumaraswamy (TKw) G family, for modeling life testing problems, which is obtained by using the quadratic rank transmutation map method, which possesses a bathtub shape for its hazard rate.
Journal ArticleDOI
Kumaraswamy Exponentiated Chen Distribution for Modelling Lifetime Data
TL;DR: In this paper, the authors introduced the Kumaraswamy exponentiated Chen distribution for modeling a bathtub-shaped hazard rate function, and the method of maximum likelihood was used for estimating the model parameters.
Journal ArticleDOI
The Zografos-Balakrishnan Odd Log-Logistic Generalized Half-Normal Distribution with Mathematical Properties and Simulations
TL;DR: In this paper, a new class of distributions called the Zografos-Balakrishnan odd log-logistic Generalized half-normal (ZOLL-GHN) family with four parameters is introduced and studied.
Journal ArticleDOI
The exponentiated logarithmic generated family of distributions and the evaluation of the confidence intervals by percentile bootstrap
Pedro Rafael Diniz Marinho,Gauss M. Cordeiro,Fernando Peña Ramírez,Morad Alizadeh,Marcelo Bourguignon +4 more
TL;DR: In this paper, a new generator of continuous distributions with three additional parameters, called the exponentiated logarithmic generated family, was proposed to extend the normal, Weibull, gamma and Gumbel distributions.
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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