Use of Orthogonal Polynomial Approximations for Inference in Exponential Distribution Based on K-Sample Doubly Type-II Censored Data
Authors:
Deepak Sanjel a;
N. Balakrishnan b
| Affiliations: | a Department of Mathematics and Statistics, Minnesota State University, Mankato, Minnesota, USA |
| b Department of Mathematics and Statistics, McMaster University, Hamilton, Canada |
DOI:
10.1080/03610920600920511
Publication Frequency:
20 issues per year
Published in:
Communications in Statistics - Theory and Methods,
Volume
35,
Issue
9
September
2006
, pages 1671
- 1683
Subject:
Mathematics & Statistics;
Formats available:
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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.
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| 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 |
| view references (14) |

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