A New Analytical Perspective on Product, Product of Ratio, and Ratio of Product of Lomax Random Variables

Abstract

Various methodologies are proposed in the literature for performance analysis of next-generation communication systems, which generally involve complex analysis. In this work, we propose an alternative method to analyze the system performance in a simpler and unified way based on incomplete-moment. First, we derive the probability density function (PDF) for the product, ratio of the product, and the product of ratio of the Lomax variates. The Lomax distribution has recently received attention due to its utility in the analysis of device-to-device, interference-limited environments, cooperative spectrum sensing, and ultra-reliable low-latency communication systems. Later, we propose new generalized incomplete moments, whose formulation enables simpler evaluation of performance indicators through use cases such as outage probability and generalized moments. Finally, we employ generalized incomplete-moment and their use cases to evaluate various performance metrics in communication systems, including applications in short-packet communications and physical layer security. © 2020 IEEE.