Extension of generalized integro-exponential function and its application in study of chen distribution

Abstract

In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical properties moments, quantile and generating func- tions, among others. In this article, we derive a power series expansion for newly introduced real upper parameter generalized integro-exponential func- tion Esp (z) extending certain Milgram's findings. By our novel results we derive closed-form expressions for the moments, generating function, Rényi entropy and power series for the quantile function of the Chen distribution.