A Size Biased Gamma Lindley Distribution

Abstract

The present paper offers a new extension to the gamma Lindley distribution called size-biased gamma Lindley distribution (SBGaL). Several properties of this distribution such as moment method, maximum likelihood estimation, and limiting distribution of extreme order statistics are established. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators of the parameters. Finally, an application of the model to a real data set is presented and compared with the fit attained by some other well-known two (three)-parameter distributions.