Comparison of estimation methods for unit-Gamma distribution

Sanku Dey ； Andre F. B. Menezes ； Josmar Mazucheli

《Journal of Data Science》 17卷4期 (2019/10) Pp. 768-801

https://doi.org/10.6339/JDS.201910_17(4).0009

摘要

In this study we have considered different methods of estimation of the unknown parameters of a two-parameter unit-Gamma (UG) distribution from the frequentists point of view. First, we briefly describe different frequentists approaches: maximum likelihood estimators, moments estimators, least squares estimators, maximum product of spacings estimators, method of Cramer-von-Mises, methods of Anderson- Darling and four variants of Anderson-Darling test and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The performances of the estimators have been compared in terms of their bias and root mean squared error using simulated samples. Also, for each method of estimation, we consider the interval estimation using the bootstrap method and calculate the coverage probability and the average width of the bootstrap confidence intervals. The study reveals that the maximum product of spacing estimators and Anderson-Darling 2 (AD2) estimators are highly competitive with the maximum likelihood estimators in small and large samples. Finally, two real data sets have been analyzed for illustrative purposes.

關鍵字

Unit-Gamma distribution ； Monte Carlo simulations ； Estimation methods ； Parametric bootstrap methods