Bayesian inference from the Kumaraswamy-Weibull distribution with applications to real data

Mandouh, R. M.

doi:10.12988/ijcms.2016.51162

Cited by 3 publications

(3 citation statements)

References 5 publications

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“…The KumW distribution has been considered by some authors, for example, [ 22 , 23 ] discussed different types of statistical inference for constant stress accelerated life tests based on censored sampling data from the KumW distribution. [ 24 ] discussed some Bayesian analyses for the KumW distribution. [ 25 ] considered a regression model for bivariate random variables based on the bivariate KumW distribution.…”

Section: Introductionmentioning

confidence: 99%

Survival analysis of cancer patients using a new extended Weibull distribution

Klakattawi

2022

PLoS ONE

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One of the most important applications of statistical analysis is in health research and applications. Cancer studies are mostly required special statistical considerations in order to find the appropriate model for fitting the survival data. Existing classical distributions rarely fit such data well and an increasing interest has been shown recently in developing more flexible distributions by introducing some additional parameters to the basic model. In this paper, a new five-parameters distribution referred as alpha power Kumaraswamy Weibull distribution is introduced and studied. Particularly, this distribution extends the Weibull distribution based on a novel technique that combines two well known generalisation methods, namely, alpha power and T-X transformations. Different characteristics of the proposed distribution, including moments, quantiles, Rényi entropy and order statistics are obtained. The method of maximum likelihood is applied in order to estimate the model parameters based on complete and censored data. The performance of these estimators are examined via conducting some simulation studies. The potential importance and applicability of the proposed distribution is illustrated empirically by means of six datasets that describe the survival of some cancer patients. The results of the analysis indicated to the promising performance of the alpha power Kumaraswamy Weibull distribution in practice comparing to some other competing distributions.

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Section: Introductionmentioning

confidence: 99%

Survival analysis of cancer patients using a new extended Weibull distribution

Klakattawi

2022

PLoS ONE

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“…Cordeiro et al (2010) showed the availability and flexibility of the estimation using the KW model by the maximum likelihood (ML) method. The Bayes estimates for the parameters of the distribution using the Gibbs sampling procedure are obtained by Mandouh (2016). Mandouh (2016) adopted a non-informative prior that gives little information about the parameters, a priori, and inexact hyperparameters.…”

Section: Introductionmentioning

confidence: 99%

“…The Bayes estimates for the parameters of the distribution using the Gibbs sampling procedure are obtained by Mandouh (2016). Mandouh (2016) adopted a non-informative prior that gives little information about the parameters, a priori, and inexact hyperparameters. The main aims of the work are: (1) To propose the simplest form for Lindley approximation of the posterior mean, (2) To examine the performances of the approximate Lindley estimators in the case of the multiparameter model such as Kumaraswamy Weibull; and (3) To show the capability and flexibility of using the KW distribution for estimation using the wellknown Bayesian methods (Huber and Train, 2001) under two loss functions.…”

Section: Introductionmentioning

confidence: 99%

Lindley procedure and MCMC technique in Bayesian estimation for Kumaraswamy Weibull distribution

Eissa¹

2022

Int. j. adv. appl. sci.

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In this study, a comparison between three methods for estimating unknown parameters of the Kumaraswamy Weibull distribution for different sample sizes of type II censoring data is presented. Specifically, we compare the behaviors of maximum likelihood estimates, Lindley and Markov chain Monte Carlo (MCMC) estimates as Bayesian estimates. We have not found any work on this topic after reviews of the literature except one with little information about the inference of this important distribution. The simplest form for Lindley approximation of the posterior mean is proposed and approximate closed forms of acceptable Bayes estimates for the models of multi-parameters such as Kumaraswamy Weibull distribution is derived. A Monte Carlo simulation is conducted to investigate the performances of the proposed estimators. Finally, three real data examples are analyzed to illustrate the application possibility of the different proposed estimation methods. The results reveal that, although, good performance of the approximate forms of Lindley estimators, the estimators resulting in the MCMC technique are better in the sense of the mean squared errors.

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Bayesian inference from the Kumaraswamy-Weibull distribution based on censored samples with applications real data

Mandouh¹

2016

ijcms

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This paper is concerned with the Bayesian analysis for the Kumaraswamy-Weibull (Kum-W) distribution under type II censored samples. Approximate Bayes estimates are computed using the Gibbs sampling procedure. This procedure generates samples from the posterior distributions. The approximate Bayes estimators are obtained under the assumptions of non-informative priors. Also, using Bayesian framework, the posterior density function, the predictive density for a single future response, i th ordered future response, and several future responses are derived under type II doubly censored samples. The predictive means, standard deviations, prediction intervals, and the shape characteristics for a single future response are determined. Applications to real data sets are utilized to illustrate the potentiality of the Bayesian analysis and the predictive results.

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Bayesian inference from the Kumaraswamy-Weibull distribution with applications to real data

Cited by 3 publications

References 5 publications

Survival analysis of cancer patients using a new extended Weibull distribution

Survival analysis of cancer patients using a new extended Weibull distribution

Lindley procedure and MCMC technique in Bayesian estimation for Kumaraswamy Weibull distribution

Bayesian inference from the Kumaraswamy-Weibull distribution based on censored samples with applications real data

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