An improved approximation for the Nakagami-m inverse CDF using artificial bee colony optimization

Abstract

The quantile function [or inverse cumulative distribution function (CDF)] is a probabilistic measure that is widely employed in both statistical applications and Monte Carlo methods. In addition, this function is important to determine performances of the communication systems, especially for wireless communication systems. However, numerical computing of the Nakagami-m inverse CDF is quite difficult because of the fact that a closed-form expression of the Nakagami-m inverse CDF is not available. In this paper, an improved expression for the Nakagami-m inverse CDF is presented by using curve-fitting methods. Furthermore, parameters of the proposed mathematical model are optimized by the help of artificial bee colony algorithm that is a population based meta-heuristic optimization method motivated by the foraging behavior of honey bee swarms. The results acquired by the proposed approximation are also compared with other existing approaches in the literature in terms of complexity and performance. It is shown that the presented approximation is more accurate, simple and effective against to the previously reported approximations.