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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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30 Apr 2020
TL;DR: In this paper, a generalized version of the Pareto distribution using the Kumaraswamy method was proposed, and a detailed account of the general mathematical properties of the new generalized distribution is presented.
Abstract: In this study, a new generalization of the Pareto distribution is undertaken, by first generalizing the Pareto distribution using the Kumaraswamy method and thereafter transmuting the resulting Kumaraswamy Pareto distribution. A detailed account of the general mathematical properties of the new generalized distribution is presented. The shapes of the Transmuted Kumaraswamy Pareto Density were plotted using R-program. The results show the superiority of the Transmuted Kumaraswamy Pareto distribution over the one parameter Pareto distribution.
Journal ArticleDOI
31 Dec 2019
TL;DR: In this article, the authors used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters  θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition, they used method of moments for estimating the parameters of the prior distributions.
Abstract: Accepted: 17/2/2019 Abstract In this paper, we used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters  θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition to that we used method of moments for estimating the parameters of the prior distributions. Bayes estimators derived under the squared error loss function. We conduct simulation study, to compare the performance for each estimator, several values of the shape parameter (θ) from Kumaraswamy distribution for data-generating, for different samples sizes (small, medium, and large). Simulation results have shown that the Best method is the Bayes estimation according to the smallest values of mean square errors(MSE) for all samples sizes (n).
Journal ArticleDOI
TL;DR: The moments, the moment-generating function and the failure rate function are derived, and the identifiability of the class of all finite mixtures of Kumaraswamy distributions is proved.
Abstract: Heterogeneous real datasets need complex probabilistic structures for a correct modeling. On the other hand, several generalizations of the Kumaraswamy distribution have been developed in the past few decades in an attempt to obtain better data adjustments that are limited in the interval (0,1). In this paper, we propose a mixture model of Kumaraswamy distributions (MMK) as a probabilistic structure for heterogeneous datasets with support in (0,1) and as an important generalization of the Kumaraswamy distribution. We derive the moments, the moment-generating function and analyze the failure rate function. Also, we prove the identifiability of the class of all finite mixtures of Kumaraswamy distributions. Via the EM-algorithm, we find estimates of maximum likelihood for the parameters of the MMK. Finally, we test the performance of the estimates by Monte Carlo simulation and illustrate an application of the proposed model using a real dataset.
Journal ArticleDOI
TL;DR: In this paper, the maximum likelihood estimator of conditional stress-strength models, asymptotic distribution of this estimator, and its confidence intervals are obtained for Kumaraswamy distribution.
Abstract: Stress-strength models have been frequently studied in recent years. An applicable extension of these models is conditional stress-strength models. The maximum likelihood estimator of conditional stress-strength models, asymptotic distribution of this estimator, and its confidence intervals are obtained for Kumaraswamy distribution. In addition, Bayesian estimation and bootstrap method are applied to the model.
Journal ArticleDOI
TL;DR: In this article, a class of modified power series inverted exponentiated generalized distributions is introduced and some characterization theorems are also presented, where the power series family is considered and some properties of the inverted Kumaraswamy distribution are investigated.
Abstract: Within the master thesis [1], the author considered the following random variable $$T=X^{-1}-1$$ where $X$ follows the Kumaraswamy distribution, and obtains a so-called inverted Kumaraswamy distribution, and studies some properties and applications of this class of distributions in the context of the power series family [2]. Within the paper [3], they introduced the exponentiated generalized class of distributions and obtained some properties with applications. Based on these developments we introduce a class of modified power series inverted exponentiated generalized distributions and obtain some of their properties with applications. Some characterization theorems are also presented. Avenues for further research concludes the paper.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
202124
202033
201925
201820
201729