Inferences for Weibull Fréchet Distribution Using a Bayesian and Non-Bayesian Methods on Gastric Cancer Survival Times.

Rashad M El-Sagheer,Mohamed A W Mahmoud,Ethar M Shokr,Beih S El-Desouky,Nadia A Chuzhanova

doi:10.1155/2021/9965856

Rashad M El-Sagheer, Mohamed A W Mahmoud + Show 3 more

Open Access

https://doi.org/10.1155/2021/9965856

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Abstract

In this article, based on progressively type-II censored schemes, the maximum likelihood, Bayes, and two parametric bootstrap methods are used for estimating the unknown parameters of the Weibull Fréchet distribution and some lifetime indices as reliability and hazard rate functions. Moreover, approximate confidence intervals and asymptotic variance-covariance matrix have been obtained. Markov chain Monte Carlo technique based on Gibbs sampler within Metropolis–Hasting algorithm is used to generate samples from the posterior density functions. Furthermore, Bayesian estimate is computed under both balanced square error loss and balanced linear exponential loss functions. Simulation results have been implemented to obtain the accuracy of the estimators. Finally, application on the survival times in years of a group of patients given chemotherapy and radiation treatment is presented for illustrating all the inferential procedures developed here.

Highlights

In recent years, the experiments that it results survival data are less preferred because of being time consuming and expensive
We computed the Bayes estimates based on 10000 Markov chain Monte Carlo technique (MCMC) samples with respect to the BSE and BLINEX loss function are computed for two distinct values of ω, equal 0 and 0.6
The performance of the resulting estimators of a, b, α, β, rðtÞ, and hðtÞ has been considered in terms of mean square error (MSE), which is computed by MSE = 1/M∑Mi=1 ðψ∧ik − ψkÞ2, k = 1, 2, ⋯, 6 and ψ1 = a, ψ2 = b, ψ3 = α, ψ4 = β, ψ5 = rðtÞ, and ψ6 = hðtÞ

Summary

Introduction

The experiments that it results survival data are less preferred because of being time consuming and expensive. Type-I and type-II are the two basic censored schemes In these schemes, the life testing experiment terminates at a prespecified time T and number of failures m, respectively. The main drawback of them is that it does not apply to all removal points until termination points For this reason, progressive censoring is proposed. In progressive type-I censoring scheme, let n be the sample size used in the experiment. In this censoring scheme, R1, R2, ⋯, Rm are the number of items which randomly withdrawn at time points T1, T2, ⋯, Tm, respectively, and the test will be terminated at Tm. we describe progressive type-II censoring scheme.

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