Estimation under modified Weibull distribution based on right censored generalized order statistics |
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Authors: | Saieed F Ateya |
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Institution: | 1. Mathematics &2. Statistics Department, Faculty of Science, Taif University, Taif, Saudi Arabia |
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Abstract: | In this paper, the maximum likelihood (ML) and Bayes, by using Markov chain Monte Carlo (MCMC), methods are considered to estimate the parameters of three-parameter modified Weibull distribution (MWD(β, τ, λ)) based on a right censored sample of generalized order statistics (gos). Simulation experiments are conducted to demonstrate the efficiency of the proposed methods. Some comparisons are carried out between the ML and Bayes methods by computing the mean squared errors (MSEs), Akaike's information criteria (AIC) and Bayesian information criteria (BIC) of the estimates to illustrate the paper. Three real data sets from Weibull(α, β) distribution are introduced and analyzed using the MWD(β, τ, λ) and also using the Weibull(α, β) distribution. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic, {AIC and BIC} to emphasize that the MWD(β, τ, λ) fits the data better than the other distribution. All parameters are estimated based on type-II censored sample, censored upper record values and progressively type-II censored sample which are generated from the real data sets. |
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Keywords: | modified Weibull distribution generalized order statistics maximum likelihood estimation Bayes estimation Gibbs sampler Metropolis–Hastings algorithm MCMC algorithm K–S test statistic Akaike's information criteria (AIC) Bayesian information criteria (BIC) |
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