Parametric inference of Akash distribution for Type-Ⅱ censoring with analyzing of relief times of patients

<abstract><p>In this paper, the problem of estimating the parameter of Akash distribution applied when the lifetime of the product follow Type-Ⅱ censoring. The maximum likelihood estimators (MLE) are studied for estimating the unknown parameter and reliability characteristics. Approximate confidence interval for the parameter is derived under the s-normal approach to the asymptotic distribution of MLE. The Bayesian inference procedures have been developed under the usual error loss function through Lindley's technique and Metropolis-Hastings algorithm. The highest posterior density interval is developed by using Metropolis-Hastings algorithm. Finally, the performances of the different methods have been compared through a Monte Carlo simulation study. The application to set of real data is also analyzed using proposed methods.</p></abstract>

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Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

Journal of Reliability and Statistical Studies ◽

10.13052/10.13052/jrss0974-8024.14212 ◽

2021 ◽

Author(s):

Hiba Zeyada Muhammed ◽

Essam Abd Elsalam Muhammed

Keyword(s):

Monte Carlo ◽

Real Data ◽

Posterior Density ◽

Data Set ◽

Bayes Estimates ◽

Squared Error ◽

Distribution Shape ◽

Highest Posterior Density Intervals ◽

Metropolis Hasting Algorithm ◽

Highest Posterior Density

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

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A bivariate Pareto type I models

International Journal of Advanced Statistics and Probability ◽

10.14419/ijasp.v5i1.7638 ◽

2017 ◽

Vol 5 (1) ◽

pp. 44

Author(s):

Mervat Abd Elaal ◽

Hind Alzahrani

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Maximum Likelihood ◽

Simulation Study ◽

Real Data ◽

Type I ◽

Data Set ◽

Monte Carlo Simulation Study ◽

Bayesian Estimations

In this paper two new bivariate Pareto Type I distributions are introduced. The first distribution is based on copula, and the second distribution is based on mixture of and copula. Maximum likelihood and Bayesian estimations are used to estimate the parameters of the proposed distribution. A Monte Carlo Simulation study is carried out to study the behavior of the proposed distributions. A real data set is analyzed to illustrate the performance and flexibility of the proposed distributions.

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Estimation of Stress Strength Reliability of Inverse Weibull Distribution under Progressive First Failure Censoring

Austrian Journal of Statistics ◽

10.17713/ajs.v47i4.638 ◽

2018 ◽

Vol 48 (1) ◽

pp. 14-37

Author(s):

Hare Krishna ◽

Madhulika Dube ◽

Renu Garg

Keyword(s):

Monte Carlo ◽

Real Life ◽

Credible Interval ◽

Estimation Methods ◽

Posterior Density ◽

Monte Carlo Simulation Study ◽

Scale Parameters ◽

Real Life Data ◽

Inverse Weibull Distribution ◽

Highest Posterior Density

In this article, estimation of stress-strength reliability $\delta=P\left(Y<X\right)$ based on progressively first failure censored data from two independent inverse Weibull distributions with different shape and scale parameters is studied. Maximum likelihood estimator and asymptotic confidence interval of $\delta$ are obtained. Bayes estimator of $\delta$ under generalized entropy loss function using non-informative and gamma informative priors is derived. Also, highest posterior density credible interval of $\delta$ is constructed. Markov Chain Monte Carlo (MCMC) technique is used for Bayes computation. The performance of various estimation methods are compared by a Monte Carlo simulation study. Finally, a pair of real life data is analyzed to illustrate the proposed methods of estimation.

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