The distribution of the sum of independent and non identically generalized Lindley random variables

Abstract

The original or generalized Lindley distribution has been proposed in order to fit a stochastic model to real data, that is, it establishes the distribution of the sum of independent variables. The distribution of the sum of independent and non identically generalized Lindley random variables is obtained by using inverse transformation of the moment generating function. A saddlepoint and a normal approximations are used to approximate the derived distribution. The accuracy of the approximations is shown by numerical simulations.

Keywords:

• Confluent hypergeometric function
• Lindley distribution
• moment generating function
• saddlepoint approximation

Acknowledgments

The authors wish to express sincere thanks to the editor and the anonymous referee, whose comments improve the quality of the manuscript.