This paper presents a comprehensive statistical analysis of the characteristics of wideband channel gains in underwater acoustic environments. Through empirical data generation, we examine the underwater wideband channel gains and subsequently employ curve fitting techniques to assess their conformity with log-normal, gamma, Weibull, Nakagami, and Rayleigh distributions. The investigation encompasses sound speed profiles from 30 distinct geographical coordinates situated within the Indian Ocean, reaching depths of up to 2 km. To simulate the stochastic sea surface, we utilize the Pierson-Moskowitz spectral model for fully developed wind. Furthermore, the random bottom surface is modeled as a sinusoidal topology with hills rising to a maximum of 10 meters in height. Statistical assessments, namely the mean square error and the coefficient of determination, are employed to quantitatively evaluate the quality of fit. The findings indicate that the log-normal distribution demonstrates the highest degree of fit.