Prediction Bounds for the Weibull Distribution

by Ananda A. Jayawardhana and V.A. Samaranayake.

Abstract: An approximate method for constructing prediction limits for a future Weibull observation, based on the Maximum Likelihood Predictive Density approach proposed by Lejeune and Faulkenberry (1982), is derived. It is proposed as a simple and versatile alternative to existing methods, with prediction bounds given by easily computable closed form expressions. The proposed procedure can be adapted to obtaining both upper and lower prediction bounds under either Type I or Type II censoring schemes. Results of a Monte Carlo simulation study that compares the coverage probabilities of the proposed method and several modified versions are given. It is shown that the proposed method provides close to nominal coverage probabilities in many instances and the modified versions can be used in its place in situations where its coverage is liberal.

Key Words: Prediction Limits, Weibull Distribution, Profile Likelihood, Type I censoring, Type II censoring

Authors:
Ananda Jayawardhana, ananda@pittstate.edu
V. A. Samaranayake, vsam@umr.edu

Editor: Mohammed Ageel,MIAQEEL@kku.edu.sa

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