In the field of the wind energy conversion, a precise determination of the probability distribution of wind speed guarantees an efficient use of the wind energy and enhances the position of wind energy against other forms of energy. The present study thus proposes utilizing an accurate numerical-probabilistic algorithm which is the combination of the Newton’s technique and the maximum entropy (ME) method to determine an important distribution in the renewable energy systems, namely the hyper Rayleigh distribution (HRD) which belongs to the family of Weibull distribution. The HRD is mainly used to model the wind speed and the variations of the solar irradiance level with a negligible error. The purpose of this research is to find the unique solution to an optimization problem which occurs when maximizing Shannon’s entropy. To confirm the accuracy and efficiency of our algorithm, we used the long-term data for the average daily wind speed in Toyokawa for 12 yr to examine the Rayleigh distribution (RD). This data set was obtained from the National Climatic Data Center (NCDC) in Japan. It seems that the RD is more closely fitted to the data. In addition, we presented different simulation studies to check the reliability of the proposed algorithm.