Prediction Based on Generalized Order Statistics from a Mixture of Rayleigh Distributions Using MCMC Algorithm

Abstract

This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper

One- and Two-Sample Predictions Based on Progressively Type-II Censored Carbon Fibres Data Utilizing a Probability Model

“…Also, many authors have focused on the problem of predicting either TSP or OSP and TSP together based on various types of censored data from different lifetime models, see, for example, Mahmoud et al [ 14 ], EL-Sagheer [ 15 ], Ahmed [ 16 ], and Abushal and Al-Zaydi [ 17 , 18 ].…”

Bayesian Prediction of Future Generalized Order Statistics from a Class of Finite Mixture Distributions

“…Equation(41)in Equation(30) and solving, numerically, Equations(31) and(32) we can obtain the lower and upper bounds of BPI.…”

“…For a given values of the prior parameters , for 1, we generate a doubly type II sample from a mixture of two ( ) 95% BPI for the observations from a future independent sample of size N are obtained by solving numerically, Equations(31) and(32) with 0.95 τ = Generate 10,000 samples each of size N from a mixture of two ( ) j Gomp α components, then calculate the coverage percentage of b Y . Different sample sizes n and N are considered.…”