Tolerance limits for gamma distribution based on generalized fiducial method

Abstract

This study proposes methods for constructing tolerance limits for the gamma distribution. The gamma distribution is found to be useful in many areas and the tolerance limits are often desirable in some monitoring and control problems. Existing inference methods either assume some parameters known or do not work well for one-sided tolerance limit case. In this study, the generalized fiducial method is used for constructing the tolerance limits for the gamma distribution. The proposed methods are assessed by a simulation study. An illustrative example demonstrates the inference methods.

Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros

“…Fluctuating rainfall makes it difficult to predict heavy precipitation that could lead to crop loss or damage. Since environmental data, meteorology, climatology and pollution studies are often right-skewed, the gamma distribution is commonly used to model these data ( Piao & Zhi-Sheng, 2015 ; Pradhan & Kundu, 2011 ; Son & Oh, 2006 ; Wang et al, 2019 ). Many researchers have developed confidence intervals for the parameters of a gamma distribution by using various methods.…”