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Abstract:
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In this article, we propose inferential procedures for a gamma distribution using the Wilson-Hilferty normal approximation. We propose normal based approaches for a gamma distribution (i) for constructing prediction limits, one-sided tolerance limits and tolerance intervals, (ii) for obtaining upper prediction limits for at least l of m observations from a gamma distribution at each of r locations, and (iii) for 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 the above problems. For each of the problems considered, the results are illustrated using practical examples.
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