Bootstrap Intervals for the Mean of the Weighted Mixture Generalized Gamma Distribution
Patchanok Srisuradetchai, Wikanda Phaphan · Lobachevskii Journal of Mathematics · 2023
The weighted mixture generalized gamma distribution (WMGG) is derived by combining two distributions, namely the generalized gamma distribution and the length-biased generalized gamma distribution, which are suitable for analyzing lifetime data. This article introduces three bootstrap methods, namely PB (Percentile Bootstrap), SB (Simple Bootstrap), and BCa (Bias-Corrected and Accelerated), for estimating the confidence interval of the mean of the WMGG distribution. In terms of simulation results, it was discovered that the coverage probabilities obtained using all three methods were far smaller than the predetermined criterion of 0.95 for sample sizes 15, 30, and 50. However, once the sample size is large enough ( $$n\geq 200$$ ), there were negligible differences in the coverage probabilities obtained through these three bootstrap methods, and their coverage probabilities approached the predetermined level of 0.95. The findings also indicate that the BCa, PB, and SB methods yielded equal average lengths across all sample sizes and parameter values examined in the simulation study. Nevertheless, in terms of coverage probability, the PB method outperformed the other methods in the majority of the simulation studies.