Shrinkage Estimators for the Exponential Scale Parameter under Multiply Type II Censoring

Umesh Singh,Anil Kumar

doi:10.17713/ajs.v34i1.397

Abstract

We consider the problem of estimating the scale parameter of an exponential distribution under multiply type II censoring when a prior point guess of the parameter value is available. Shrinkage estimators are obtained from the approximate maximum likelihood estimators proposed in Singh et al. (2004) and in Balasubramanian and Balakrishnan (1992). These estimators are then compared by their simulated mean squared errors.

Highlights

In life testing experiments a fixed number of items, say n, is often put on test simultaneously
If mid censoring arises amongst doubly censored observations, the scheme is known as a multiply type II censoring scheme
The purpose of this paper is to study the procedures, which answer the above questions in order to estimate the scale parameter of an exponential distribution under a multiply type II censoring scheme

Summary

Introduction

In life testing experiments a fixed number of items, say n, is often put on test simultaneously. It may be recalled that Thompson (1968) was the first who proposed a procedure popularly known as shrinkage procedure, which suggests the use of a prior point guess of the parameter for improving the performance of the existing estimator θ. Using Thompson’s technique, the respective shrinkage estimators based on the approximate maximum likelihood estimators θUA and θBL can be defined Studies of such types of other estimators reveal that these perform better than the original estimators provided the true value of θ is close to θ0 and α is taken to be large. Singh et al (2004) proposed a procedure to obtain an approximate maximum likelihood estimator as an alternative to the one given in Balasubramanian and Balakrishnan (1992).

Shrinkage Estimation

Specified Confidence

Unspecified Confidence

Illustrative Example

Conclusion