Topic
Kumaraswamy distribution
About: Kumaraswamy distribution is a research topic. Over the lifetime, 213 publications have been published within this topic receiving 3393 citations. The topic is also known as: Kumaraswamy's double bounded distribution.
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TL;DR: In this paper, a five-parameter Kumaraswamy Burr XII (KwBXII) distribution is defined and studied, which contains some well-known distributions discussed in lifetime literature, such as the logistic, Weibull and Burr XII distributions.
Abstract: For the first time, a five-parameter distribution, called the Kumaraswamy Burr XII (KwBXII) distribution, is defined and studied. The new distribution contains as special models some well-known distributions discussed in lifetime literature, such as the logistic, Weibull and Burr XII distributions, among several others. We obtain the complete moments, incomplete moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves and reliability of the KwBXII distribution. We provide two representations for the moments of the order statistics. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the KwBXII distribution. Three applications to real data sets demonstrate the usefulness of the proposed distribution and that it may attract wider applications in lifetime data analysis.
91 citations
TL;DR: The well-established and widely-accepted G families of distributions like the exponentiated family, Marshall-Olkin extended family, beta-generated family, McDonald-generalized family, Kumaraswamy- generalized family and exponentiated generalized family are discussed.
Abstract: The art of parameter(s) induction to the baseline distribution has received a great deal of attention in recent years. The induction of one or more additional shape parameter(s) to the baseline distribution makes the distribution more flexible especially for studying the tail properties. This parameter(s) induction also proved helpful in improving the goodness-of-fit of the proposed generalized family of distributions. There exist many generalized (or generated) G families of continuous univariate distributions since 1985. In this paper, the well-established and widely-accepted G families of distributions like the exponentiated family, Marshall-Olkin extended family, beta-generated family, McDonald-generalized family, Kumaraswamy-generalized family and exponentiated generalized family are discussed. We provide lists of contributed literature on these well-established G families of distributions. Some extended forms of the Marshall-Olkin extended family and Kumaraswamy-generalized family of distributions are proposed.
90 citations
TL;DR: The Kumaraswamy Marshal-Olkin generalized family of distributions as discussed by the authors is a family of continuous distributions with a density function that is symmetric, left-skewed, right-skedwed and reversed-J shaped.
90 citations
TL;DR: In this article, the first and second moments of the storage state distribution in terms of the moment of the inflow distribution are derived for specified drafts, using a non-linear solver.
88 citations
TL;DR: In this article, a five-parameter lifetime model called the McDonald Weibull distribution was proposed to extend the Weibell, exponentiated Weibll, beta Weiball, and Kumaraswamy Weibbull distributi...
Abstract: For the first time, we propose a five-parameter lifetime model called the McDonald Weibull distribution to extend the Weibull, exponentiated Weibull, beta Weibull and Kumaraswamy Weibull distributi...
78 citations