Prediction Intervals for Future Order Statistics from Generalized Modified Weibull Distribution

• Activity Number: 134
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Yuhlong Lio*+ and Yu-Jau Lin and H. M. Okasha
• Companies: University of South Dakota and Chung Yuan Christian University and Department of Statistics
• Keywords: Bayesian prediction ; Metropolish-Hastings Algorithm ; Gibbs Schemes

Abstract

In this talk, several Bayesian approaches to predict future order statistics based on type II censored order statistics,X_{1}< X_{2}< ...< X_{r}, of a sample with size n(>r) that comes from the four-parameter generalized modified Weibull (GMW) distribution are studied. The four parameters of GMW distribution are first estimated by the Metropolis-Hastings (M-H) algorithm with different loss functions. Then various techniques, including the method that inverts the conditional CDF of order statistics X_{i}, Monte Carlo method and MCMC procedure, are developed to predict intervals of unobserved order statistics that are viewed as latent variables in the Gibbs sampling scheme. An intensive simulation and two examples for numerical study are conducted to illustrate the prediction procedures.