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.

Some uses of orthogonal polynomials in statistical inference

“…More recent results include among others: applications in correspondence analysis Beh, 9 D'Ambra et al, 10 and Beh and Lombard, 11 birth and death processes Guillemin and Pinchon, 12 goodness‐of‐fit tests for parametric regression models Bar‐Hen and Daudin, 13 inference in the exponential distribution based on k ‐sample doubly type‐II censored data Sanjel and Balakrishnan, 14 Gibbs sampling Diaconis et al, 15 multiple correspondence analysis for ordinal‐scale variables Lombardo and Beh, 16,17 reweighted smooth tests of goodness of fit De Boeck et al, 18 study of dependence between ordinal‐nominal categorical variables in Lombardo et al, 19 canonical correlations for Dirichlet measures in Griffiths and Spano, 20 to adjust the hyperbolic secant and logistic distributions to analyze financial asset returns in Bagnato et al, 21 a general method of calculus in Withers and Nadarajah 22 …”