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Normal-based methods for a gamma distribution.

Authors
Krishnamoorthy-K; Mathew-T; Mukherjee-S
Source
Technometrics 2008 Feb; 50(1):69-78
NIOSHTIC No.
20044431
Abstract
In this article we propose inferential procedures for a gamma distribution using the Wilson-Hilferty (WH) normal approximation. Specifically, using the result that the cube root of a gamma random variable is approximately normally distributed, we propose normal-based approaches for a gamma distribution for (a) constructing prediction limits, one-sided tolerance limits, and tolerance intervals; (b) for obtaining upper prediction limits for at least l of m observations from a gamma distribution at each of r locations; and (c) assessing the reliability of a stress-strength model involving two independent gamma random variables. For each problem, a normal-based approximate procedure is outlined, and its applicability and validity for a gamma distribution are studied using Monte Carlo simulation. Our investigation shows that the approximate procedures are very satisfactory for all of these problems. For each problem considered, the results are illustrated using practical examples. Our overall conclusion is that the WH normal approximation provides a simple, easy-to-use unified approach for addressing various problems for the gamma distribution.
Keywords
Models; Statistical-analysis; Monitors; Monitoring-systems; Mathematical-models; Industrial-hygiene; Samplers; Sampling; Author Keywords: Confidence limits; Coverage probability; Quantile; Survival probability; Tolerance limits; Wilson-Hilferty approximation
Contact
K. Krishnamoorthy, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70508
CODEN
TCMTA2
Publication Date
20080201
Document Type
Journal Article
Email Address
krishna@louisiana.edu
Funding Type
Grant
Fiscal Year
2008
NTIS Accession No.
NTIS Price
Identifying No.
Grant-Number-R01-OH-003628
Issue of Publication
1
ISSN
0040-1706
Source Name
Technometrics
State
MD; LA
Performing Organization
University of Maryland, Baltimore
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