Joint Statistics of Partial Sums of Ordered i.n.d. Gamma Random Variables

Sung Sik Nam, Changseok Yoon and Seyeong Choi ()
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Sung Sik Nam: Department of Electronic Engineering, Gachon University, Seongnam-si 13102, Republic of Korea
Changseok Yoon: Smart Network Research Center, Electronics Center, Korea Electronics Technology Institute, 1599 Sangam-dong, Mapo-gu, Seoul 03924, Republic of Korea
Seyeong Choi: Department of Information and Communication Engineering, Wonkwang University, Iksan-si 54538, Republic of Korea

Mathematics, 2023, vol. 11, issue 20, 1-18

Abstract: From the perspective of wireless communication, as communication systems become more complex, order statistics have gained increasing importance, particularly in evaluating the performance of advanced technologies in fading channels. However, existing analytical methods are often too complex for practical use. In this research paper, we introduce innovative statistical findings concerning the sum of ordered gamma-distributed random variables. We examine various channel scenarios where these variables are independent but not-identically distributed. To demonstrate the practical applicability of our results, we provide a comprehensive closed-form expression for the statistics of the signal-to-interference-plus-noise ratio in a multiuser scheduling system. We also present numerical examples to illustrate the effectiveness of our approach. To ensure the accuracy of our analysis, we validate our analytical results through Monte Carlo simulations.

Keywords: order statistics; joint statistics; gamma distribution; non-identical distribution; moment generating function; cumulative distribution function; probability density function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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