Confidence interval estimation for the difference of censored zero-inflated gamma distributions

Abstract

Abstract This paper studies the problem of constructing confidence intervals (CIs) for the difference between coefficients of variation (CV) of two censored zero-inflated gamma distributions. Firstly, we propose a Fiducial inference based method that extends the traditional CI construction method of gamma distribution to the scenario of zero-inflated gamma distributions with censored data. Secondly, we propose a Box-Cox transformation based method, in which not only the sample data needs to be transformed, but also the detection limit of gamma distribution with censored data accordingly. Thirdly, we investigate the Method of Variance Estimate Recovery (MOVER), to combine the previous two gamma distribution CI estimates with three binomial distribution CI estimates, and obtain six combination methods. Furthermore, we conduct Monte Carlo simulations to evaluate the performances of the proposed methods, the results indicate that all CI construction methods achieve satisfactory performances in terms of coverage probability, average length and tail error rates. Finally, we perform real data analysis using 11 years of precipitation data from Zhengzhou and Lhasa.

Keywords

• Confidence interval
• Zero-inflated gamma distribution
• Censored data
• Coefficient of variation
• Detection limit
• Precipitation data