Abstract

In this article, we provide a consistent method of estimation for the parameters of a three-parameter generalized exponential distribution which avoids the problem of unbounded likelihood function. The method is based on a maximum likelihood estimation of the shape parameter, which uses location and scale invariant statistic, originally proposed by Nagatsuka et al. (A consistent method of estimation for the three-parameter weibull distribution, Computational Statistics & Data Analysis 58:210–26). It has been shown that the estimators are unique and consistent for the entire range of the parameter space. We also present a Monte-Carlo simulation study along with the comparisons with some prominent estimation methods in terms of the bias and root mean square error. For the illustration purpose, the data analysis of a real lifetime data set has been reported.

摘要

在本文中，我们提供了一种三参数广义指数分布参数的一致估计方法，避免了无界似然函数的问题。该方法基于形状参数的最大似然估计，该方法使用位置和尺度不变统计量，最初由 Nagatsuka 等人提出。（三参数威布尔分布的一致估计方法，计算统计与数据分析 58：210-26）。事实证明，估计量在参数空间的整个范围内是唯一且一致的。我们还提出了蒙特卡罗模拟研究，并在偏差和均方根误差方面与一些著名的估计方法进行了比较。为了便于说明，