Random distributions play a crucial role in optimization algorithms, providing a means to introduce randomness and exploration in the search process. This paper presents a comprehensive comparative analysis of several random distributions, including Levy, Gamma, Tangent, Rayleigh, Weibull, Cauchy, Exponential, Log-Normal, and Chi-Square distributions, and their applications in optimization algorithms. The objective is to evaluate the suitability of these distributions for different optimization problems and shed light on their strengths and limitations. The paper provides an overview of each distribution, discusses their properties, and explores their utilization in optimization algorithms. Experimental results and analysis are presented to compare the performance of these distributions in various optimization scenarios. The findings of this study will assist researchers and practitioners in selecting appropriate random distributions for optimizing diverse problem domains.