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 functions, among others. In this article, we derive a power series expansion for newly introduced real upper parameter generalized integro-exponential function E p s (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.

On the qualitative analyses solutions of new mathematical models of integro‐differential equations with infinite delay

“…Pogany et al [23] provided a power series expansion for newly introduced real upper parameter generalized integro‐exponential function Eps(z) extending certain Milgram's findings. By the novel results, Pogány et al [23] derived closed‐form expressions for the moments, generating function, Rényi entropy and power series for the quantile function of the Chen distribution.…”

Generalized Exponential Power Distribution with Application to Complete and Censored Data

“…, is an extension of generalized integroexponential function introduced by Pogany et al [20]. The function E j s (z) can be presented as…”

On Moments of Gamma—Exponentiated Functional Distribution

“…Numerous authors have linked to listed models considering special cases of Gamma generalized, exponentiated distribution classes, among others we refer to Gamma-exponentiated Weibull [9,10], exponentiated Weibull, exponentiated Pareto, exponentiated Gamma [11], Kumaraswamy generalized Gamma and Gumbel [12,13] distributions with exhaustive references lists and links to further sub-models and special cases, consult e.g., ( [13], pp. 415-416); also see the recent article [14] where an extension is obtained for the generalized integro-exponential function by which the moment expression of the above listed distribution classes can be expressed in a closed or more compact form. Finally, we mention the related recent article [15] as well.…”