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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A new method for generating families of continuous distributions
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The Kumaraswamy Weibull distribution with application to failure data
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Generalized Beta-Generated Distributions
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Generalized beta-generated distributions
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An extended Lomax distribution
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References
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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.
Generalized additive models for location, scale and shape - Discussion
TL;DR: Rigby and Stasinopoulos as mentioned in this paper proposed generalized additive models for location, scale and shape (GAMLSS), a general framework for univariate regression type statistical problems.
Journal ArticleDOI
The beta Gumbel distribution
Saralees Nadarajah,Samuel Kotz +1 more
TL;DR: In this paper, a generalization of the Gumbel distribution, referred to as the beta GUMEL distribution, is proposed. But the authors do not provide a comprehensive treatment of the mathematical properties of this new distribution.
Journal ArticleDOI
Computing the moments of order statistics from nonidentical random variables
TL;DR: In this article, the authors establish new representations, identities and recurrence relations of order statistics arising from general independent non-identically distributed random variables (r.v.’s), which enable one to compute all moments of all o.s. in a simple manner.
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