The estimation of the Burr-XII parameters with middle-censored data.

Ali H Abuzaid

doi:10.1186/s40064-015-0856-3

Abstract

Middle-censoring is considered as a modern general scheme of censoring. In this paper, we study the analysis of middle-censored data with Burr-XII distribution which is considered one of the most popular and flexible distributions for modeling stochastic events and lifetime for many products.The parameters are estimated by the maximum likelihood method and the Bayes estimation under gamma prior and by applying the Lindley’s approximation.A simulation study is carried out to compare the performances of the two estimates. Both estimators behave almost similarly and verified the consistency property. A real medical data set is considered for illustration.

Highlights

Burr (1942) constructed a system of distributions that contains twelve types
The maximum likelihood estimation (MLE) based on the iterative procedure given in (3.2, 3.3) and the Bayes estimates with respect to Squared Error Loss (SEL) and using the prior gamma with θ = 0.1 and β = 0.1 are obtained using Equations (4.6, 4.7 and 4.8)
CP is the mean of censoring percentages

Summary

Introduction

Burr (1942) constructed a system of distributions that contains twelve types. The Burr-XII distribution denoted by Burr-XII (a, b) is one of the most popular distributions due to its appropriateness for modelling stochastic events (Zimmer et al 1998) and its flexibility for representing the lifetime for many products where it has a non-monotone hazard function (Soliman 2002). A general censoring scheme, known as Middle-censoring as presented in Middle-censoring, is considered to obtain the estimation of the Burr-XII parameters with middle-censored data. We analyze the Burr-XII lifetime data when they are middle-censored. T i∉ðLi; RiÞ; otherwise: Maximum likelihood estimation Suppose that n randomly selected units from Burr-XII (a, b) population, where a and b are both unknown, are put on test under middle-censoring scheme.

Results

Conclusion