<p>It is well known that the Rician distribution models several physical and natural behaviors, such as sighting error when shooting at targets, dominant line-of-sight (LOS) fading channels in radar and wireless communications systems (WCS), and the tilt and eccentricity of the earth’s orbit in the solar system. A sum-product of distributions (SPDs) is also used to describe adding up the reflected and scattered signals. Nonetheless, deriving the probability density function (PDF) and cumulative distribution function (CDF) of SPDs in closed form is particularly challenging, especially for generalized distributions. By leveraging the properties of the Gamma function, the ratio of two consecutive moments of the Fox’s H-distribution can be simplified, making it a suitable candidate for estimating various unknown SPDs. In this context, the univariate Fox’s H-function and moment-based parameter estimators are used to get a good estimation of the PDF and CDF for the sum-product of independent and identically distributed Rician random variables. Furthermore, the absolute convergence of the associated infinite series is rigorously demonstrated to establish the validity of the density estimations. Subsequently, using the root mean square error, we show that the estimated density function converges to the simulated ones for various sample sizes. Following that, several performance measures are found for an intelligent reflecting surface-based WCS, including the average symbol error rate and outage probability. To provide deeper insights, the asymptotic behavior of the two aforementioned metrics is shown in the high signal-to-noise ratio regime. The results demonstrated that integrating an intelligent reflecting surface with a large number of reflecting elements can significantly improve the performance of a wireless network, even the obstruction of the LOS. Moreover, Monte Carlo simulations of different setups back up how tight our mathematical results are.</p>