A novel approach for parameter estimation of mixture of two Weibull distributions in failure data modeling - Yan, Tianyu; Fang, Kai-Tai; Yin, Hong (Statistics and computing, 2024)
The mixture of two 2-parameter Weibull distributions (MixW), as a specialized variant of the mixture of Weibull distributions, serves as an ideal model for heterogeneous data sets within the realms of reliability studies and survival analysis. A principal challenge in dealing with MixW lies in the estimation of parameters. Inspired by the exemplary efficacy of the Quasi-Monte Carlo method in quantile estimation, this paper introduces an innovative approach, which employs the Harrell-Davis and three Sfakianakis and Verginis quantile estimators to enhance the representativeness of the sample, thereby improving the accuracy of parameter estimation. Given the difficulty in deriving analytical expressions for the parameters of MixW and their propensity for convergence to local maxima, this paper adopts the sequential number-theoretic (SNTO) algorithm for the numerical resolution of parameter estimation. The initial optimization region for SNTO is determined via the graphical method of the Weibull probability plot. Simulation studies have demonstrated that our proposed method significantly enhances estimation precision and reduces dependence on the “quality” of the sample. Furthermore, this methodology has been applied to two real data sets that demonstrate the effectiveness of our proposed approach.