Alternative expressions of the PDF and CDF for Gamma, η−μ and κ−μ shadowed distributions with applications in wireless communications

Ferkan Yilmaz*, Mazen Omar Hasna, Khalid Qaraqe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


There are two approaches well known in the literature for reducing the complexity in averaged performance analyses of wireless communications systems (i.e., for alleviating the computational difficulty in averaged performance evaluations). The first method, known as the moment generating function MGF-based approach, aims to convert the instantaneous performance measure into an exponential integration or a certain sum of exponential functions of different scales. The second approach, which is the focus of this article, aims to convert the exact probability density function PDF and cumulative distribution function CDF of fading distributions into the sum of exponential functions of various scales. As such, we propose weighted sum of exponential functions as alternative closed-form approximations for the PDF and CDF of gamma distribution, η−μ distribution, and κ−μ shadowed distribution with integer fading parameters, and we present how these proposed expressions can be easily applied to the performance analysis of wireless communication systems operating over Nakagami-m fading channels, η−μ fading channels, and κ−μ shadowed fading channels.

Original languageEnglish
Article number101935
JournalPhysical Communication
Publication statusPublished - Feb 2023

Bibliographical note

Publisher Copyright:
© 2022 Elsevier B.V.


This publication was made possible by NPRP13S-0130-200200 from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the author[s].

FundersFunder number
Qatar National Research Fund


    • Averaged performance analysis
    • Nakagami-m fading
    • η−μ fading
    • κ−μ shadowed fading


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