Mixtures of two-component normal distributions (MixN) have various applications in statistical inference with flexibility in density fitting. The best estimation of the five model parameters still represents a challen...
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Mixtures of two-component normal distributions (MixN) have various applications in statistical inference with flexibility in density fitting. The best estimation of the five model parameters still represents a challenge. This article proposes more accurate density fittings given a random sample in both the moment-based and likelihood-based estimation frameworks. Motivated by the excellent performance of the Quasi-Monte Carlo method in quantile estimations, we propose an innovative approach to improve the accuracy of parameter estimations by reinforcing the representativeness of observed data via the distribution-free Harrell-Davis quantile estimators. The revision on the penalized maximum likelihood method is also considered due to the unpleasant properties of the original likelihood function under MixN. The bootstrap bias-corrected moment estimators are given as another revision. A sequential algorithm for optimization (snto) is conducted in finding numerical solutions for the two types of parameter estimation methods. snto is more adapted to MixN and shows strong advantages in the likelihood-based estimation compared to the famous EM algorithm. Simulation results show that our proposed approach can effectively improve estimation accuracy and increase resistance to small sample sizes and/or high percent overlaps between two mixture components. A real data example is given to illustrate the efficiency of our proposed methods.
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 stud...
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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.
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