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http://dx.doi.org/10.29220/CSAM.2020.27.6.625

Fixed-accuracy confidence interval estimation of P(X > c) for a two-parameter gamma population  

Zhuang, Yan (Department of Mathematics and Statistics, Connecticut College)
Hu, Jun (Department of Mathematics and Statistics, Oakland University)
Zou, Yixuan (Department of Statistics, University of Kentucky)
Publication Information
Communications for Statistical Applications and Methods / v.27, no.6, 2020 , pp. 625-639 More about this Journal
Abstract
The gamma distribution is a flexible right-skewed distribution widely used in many areas, and it is of great interest to estimate the probability of a random variable exceeding a specified value in survival and reliability analysis. Therefore, the study develops a fixed-accuracy confidence interval for P(X > c) when X follows a gamma distribution, Γ(α, β), and c is a preassigned positive constant through: 1) a purely sequential procedure with known shape parameter α and unknown rate parameter β; and 2) a nonparametric purely sequential procedure with both shape and rate parameters unknown. Both procedures enjoy appealing asymptotic first-order efficiency and asymptotic consistency properties. Extensive simulations validate the theoretical findings. Three real-life data examples from health studies and steel manufacturing study are discussed to illustrate the practical applicability of both procedures.
Keywords
fixed-accuracy confidence interval; gamma distribution; sequential procedure;
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