Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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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)
  • Received : 2020.07.17
  • Accepted : 2020.09.19
  • Published : 2020.11.30
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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.

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