COMPARATIVE ANALYSIS OF CONTINUOUS PROBABILITY DISTRIBUTIONS FOR MODELING MAXIMUM FLOOD LEVELS

Abstract

Probability distributions play a pivotal role in data analysis, providing insights into the likelihood of outcomes and forming the basis for statistical inference. This article explores the significance and application of various continuous probability distributions through a comprehensive comparative analysis. Using real-life data on maximum flood levels, we evaluate the efficacy of selected distributions including the Normal, Standard Normal, Cauchy, Chi-Square, and T distributions. Model selection criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Schwarz Information Criterion (SIC) are employed to assess goodness of fit and predictive capabilities. The comparative analysis reveals insights into model selection efficiency, with AIC emerging as a top performer across distributions. Notably, the Chi-Square distribution demonstrates superior performance, highlighting its potential in diverse applications. In conclusion, , it's evident that AIC outshines both SIC and BIC across all distributions analyzed in this study, also, the paper underscores the importance of selecting appropriate distributions, providing valuable insights for statistical modeling and decision-making processes across disciplines.