Stat Papers DOI 10.1007/s00362-014-0621-7 REGULAR ARTICLE Efficient estimation for the generalized exponential distribution M. Alizadeh · S. Rezaei · S. F. Bagheri · S. Nadarajah Received: 25 October 2012 / Revised: 28 July 2014 © Springer-Verlag Berlin Heidelberg 2014 Abstract In this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. The following estimators are considered: uniformly minimum variance unbiased estimator, maximum likelihood estimator, percentile estimator, least squares estimator, weighted least squares estimator and moments estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies and real data applications show that the maximum likelihood estimator performs better than others. Keywords Generalized exponential distribution · Least squares estimator · Maximum likelihood estimator · Moments estimator · Percentile estimator · Weighted least squares estimator 1 Introduction A random variable X is said to have the two-parameter generalized exponential (GE) distribution if its cumulative distribution function (CDF) and probability density func- tion (PDF) are specified by M. Alizadeh · S. Rezaei (B ) Department of Statistics, Amirkabir Unviversity of Technology, Tehran, Iran e-mail: srezaei@aut.ac.ir S. F. Bagheri Department of Mathematics, College of Basic Science, Yadegar–e-Imam Khomeini (RAH) Branch, Islamic Azad University, Tehran, Iran S. Nadarajah School of Mathematics, University of Manchester, Manchester, UK 123