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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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Journal ArticleDOI
TL;DR: This paper derives the maximum likelihood estimate of the parameters of a univariate Kumaraswamy distribution with two parameters when the available observations are described by means of fuzzy information by using Newton Raphson as well as EM algorithm method.
Abstract: Traditional statistical approaches for estimating the parameters of the Kumaraswamy distribution have dealt with precise information. However, in real world situations, some information about an underlying experimental process might be imprecise and might be represented in the form of fuzzy information. In this paper, we consider the problem of estimating the parameters of a univariate Kumaraswamy distribution with two parameters when the available observations are described by means of fuzzy information. We derive the maximum likelihood estimate of the parameters by using Newton-Raphson as well as EM algorithm method. Furthermore, we provide an approximation namely, Tierney and Kadane’s approximation, to compute the Bayes estimates of the unknown parameters. The estimation procedures are discussed in details and compared via Markov Chain Monte Carlo simulations in terms of their average biases and mean squared errors.

2 citations

Journal ArticleDOI
TL;DR: Using probability theory, the weighted version of inverted Kumaraswamy Distribution is introduced, which could be considered a better model than some other sub-models used to model Carbon fiber’s strength data.
Abstract: The procedures to discover proper new models in probability theory for different data collections are highly prevalent these days among the researchers of this area whenever existing literature models are not appropriate. Before delivering a product, manufacturers of raw materials or finished materials must follow some compliance standards in various engineering disciplines to avoid severe losses. Materials of high strength are necessary to ensure the safety of human lives along with infrastructures to elude the significant obligations linked with the provisions of non-compliant products. Using probability theory, we introduce the weighted version of inverted Kumaraswamy Distribution, which could be considered a better model than some other sub-models used to model Carbon fiber’s strength data. We derive various statistical properties of this distribution such as cumulative distribution, moments, mean residual life, reversed residual life functions, moment generating function, characteristic function, harmonic mean, and geometric mean. Parameters are estimated through the maximum likelihood method and ordinary moments. Simulation studies are carried out to illustrate the theoretical results of these two approaches. Furthermore, two real data sets of Carbon fibers strength are utilized to contrast the proposed model and its sub-models like inverted Kumaraswamy distribution and Kumaraswamy Sushila distribution through different goodness of fit criteria such as Akaike Information Criterion (AIC), corrected Akaike information criterion, and the Bayesian Information Criterion (BIC). Results reveal the outperformance of the proposed model compared to other models, which render it a proper interchange of the current sub-models.

2 citations

Journal ArticleDOI
29 May 2020
TL;DR: It is shown that the APK distribution is better than the other compared distributions fort the right-skewed data sets and could be useful to model data sets with bathtub hazard rates.
Abstract: The aim of the study is to obtain the alpha power Kumaraswamy (APK) distribution. Some main statistical properties of the APK distribution are investigated including survival, hazard rate and quantile functions, skewness, kurtosis, order statistics. The hazard rate function of the proposed distribution could be useful to model data sets with bathtub hazard rates. We provide a real data application and show that the APK distribution is better than the other compared distributions fort the right-skewed data sets.

2 citations

Journal ArticleDOI
01 Sep 2019
TL;DR: In this paper, empirical Bayes estimators of parameter, reliability and hazard function for Kumaraswamy distribution under the linear exponential loss function for progressively type II censored samples with binomial removal and type I censored samples were proposed.
Abstract: This paper proposes empirical Bayes estimators of parameter, reliability and hazard function for Kumaraswamy distribution under the linear exponential loss function for progressively type II censored samples with binomial removal and type II censored samples. The proposed estimators have been compared with the corresponding Bayes estimators for their simulated risks. The applicability of the proposed estimators have been illustrated through ulcer patient data.

2 citations

Journal ArticleDOI
TL;DR: In this article, the authors provide a comprehensive treatment of the mathematical properties of the Kumaraswamy Inverse Weibull distribution and derive expressions for its moment generating function and the $r$-th generalized moment.
Abstract: The Kumaraswamy Inverse Weibull distribution has the ability to model failure rates that have unimodal shapes and are quite common in reliability and biological studies. The three-parameter Kumaraswamy Inverse Weibull distribution with decreasing and unimodal failure rate is introduced. We provide a comprehensive treatment of the mathematical properties of the Kumaraswany Inverse Weibull distribution and derive expressions for its moment generating function and the $r$-th generalized moment. Some properties of the model with some graphs of density and hazard function are discussed. We also discuss a Bayesian approach for this distribution and an application was made for a real data set.

2 citations


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