Use of Orthogonal Polynomial Approximations for Inference in Exponential Distribution Based on K-Sample Doubly Type-II Censored Data

Abstract

Hermite and Laguerre polynomial density approximants have been utilized in order to make inference for the location and scale parameters of an exponential distribution based on K-sample Type-II censored data. First, we evaluate the exact moments of the pivots based on the Best Linear Unbiased Estimators (BLUEs) of the parameters and then, based on these moments, their density approximations are obtained using orthogonal polynomials. A comparative study of the percentiles obtained from the orthogonal polynomial approximation of the distributions of the pivots and the resulting interval estimation of the parameters to the corresponding exact numerical results of Balakrishnan and Lin (2005) and Balakrishnan et al. (2004) is carried out. A comparison is also made with the approximate inference based on the maximum likelihood estimators (MLEs) of the parameters. These comparative studies reveal that the proposed density approximant-based techniques provide very accurate inference.

Keywords:

• Best linear unbiased estimators
• Density approximants
• Doubly Type-II censored samples
• Exponential distribution
• Hermite polynomials
• Interval estimation
• Laguerre polynomials
• Maximum likelihood estimates
• Symbolic computation

Mathematics Subject Classification:

• Primary 62E17, 05E35
• Secondary 60E05, 62E15, 62N01

Acknowledgement

The financial support of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.