# Closed-Form Performance Analysis of the Inverse Power Lomax Fading Channel Model
## 1 Introduction  
Wireless communications channels' statistical description is a mature field of science and engineering that has significantly evolved during the last two decades [1, 2, 3]. This is mainly due to the rapid evolution of communication networks and systems and the necessity of high-quality predictions of their performance [4, 5, 6]. It is particularly relevant for tasks related to the analysis of ad hoc communication systems, including 5G NR [7], 6G [8], V2X [9], Wi-Fi 7 [10], Wi-Fi 8 and beyond [11], and unmanned aerial vehicle (UAV) systems [12, 13], which greatly suffer from wireless link degradation. Although a wide range of measurement campaigns has been conducted [13, 14, 15, 16, 17, 18, 19], the thickening of propagation conditions prevents the possible unification and generalization of its statistical description. An extensive growth in the number of proposed models started with the outstanding works by [PERSON] and colleagues [20, 21, 22, 23, 24] and continues to the present day with a wide range of various types, including the most intricate ones [25] and the most simplistic [26, 27]. Although these models cover a wide range of practical channels, much effort has been put into modeling heavy fading, which corresponds to poor propagation conditions. Such scenarios are generally covered by the so-called heavy-tailed distributions, with one of the most recent examples being the Lomax channel [26]. Notably, the authors in [26] specificallyfocused on the most simplistic model, but the Lomax distribution has many modifications (suitable for wireless communications) that combine both flexibility and analytical tractability. Among such modifications, one can mention the inverse power Lomax. The inverse power Lomax distribution (first proposed in [28]) is a three-parametric distribution family and was addressed for a wide range of applications related to econometrics (e.g., GDP analysis [29]), survey sampling, biological sciences (e.g., biological survival data [30]), engineering sciences (e.g., failure times for repairable items [31]), medical research (e.g., relief times analysis [28]), testing problems [32], and social and environmental sciences (e.g., school education-related problems [33] and flood discharges [34]). Moreover, the specific focus of [28] was on applications where censored data arise (with Type-I and Type-II censoring). Furthermore, it was numerously generalized, yielding more complex models, including the four-parametric model, the so-called modified alpha power transformation-inverse power Lomax [33], and the Type-II Topp-Leone modification for the IPL [35]. In spite of being widely used in various applications, its usage in communication systems design, and specifically in wireless communications, is absent. Recently, a simplified subcase of the IPL, i.e., the classical Lomax model [36], was proposed to describe the statistical effects of a fading wireless communication channel [26]. In their research, [PERSON] and [PERSON] [26] aimed to derive a simplified model capable of handling practically valuable scenarios while at the same time being analytically tractable in closed form without resorting to complex functions. It was demonstrated that all the basic statistical characteristics required for a system performance analysis (i.e., the probability density function (PDF), the cumulative distribution function (CDF) and its inverse (ICDF), its raw moments, the moment-generating function (MGF), and its generalization (GMGF)) can be expressed in closed form in contrast to some classical fading distributions (e.g., Rician, Nakagami-m, and Hoyt distributions) [26]. While defining the term \"closed-form\", the authors state that \"We take the usual convention in the literature, which considers a closed-form as that including a finite number of well-known functions [26]. This classically includes special functions like Bessel or Hypergeometric ones, but not more involved ones like Meijer-G or Fox-H functions\".