Title: A location Invariant Statistic-Based Consistent Estimation Method for Three-Parameter Generalized Exponential Distribution

Abstract: In numerous instances, the generalized exponential distribution can be used as an alternative to the gamma distribution or the Weibull distribution when analyzing lifetime or skewed data. This article offers a consistent method for estimating the parameters of a three-parameter generalized exponential distribution that sidesteps the issue of an unbounded likelihood function. The method is hinged on a maximum likelihood estimation of shape and scale parameters that uses a location-invariant statistic. Important estimator properties, such as uniqueness and consistency, are demonstrated. In addition, quantile estimates for the lifetime distribution are provided. We present a Monte Carlo simulation study along with comparisons to a number of well-known estimation techniques in terms of bias and root mean square error. For illustrative purposes, a real-world lifetime data set is analyzed.