KUMARASWAMY DISTRIBUTION AND IT'S APPLICATION

Abstract

The study delves into the practical applications of the two-parameter Kumaraswamy distribution within Monte Carlo simulation analyses. Initially, it rigorously examines the theoretical quantiles and moments of the distribution across various parameter values, revealing insights into its behavior, sensitivity to parameter changes, and tendency for skewness and leptokurtosis. This theoretical groundwork sets the stage for subsequent empirical investigations. Subsequent Monte Carlo simulations are conducted to estimate distribution parameters using both the method of moments and Maximum Likelihood Estimation (MLE). The impact of sample size variation on estimation precision is systematically analyzed, with results consistently showing that larger sample sizes lead to decreased bias and mean square error, indicative of improved precision. Comparative analysis highlights the superior performance of MLE across all sample sizes due to its robutness and efficiency in parameter estimation. In conclusion, the study underscores the versatility and efficacy of the Kumaraswamy distribution in Monte Carlo simulations, offering valuable insights into parameter estimation techniques and the distribution's statistical properties. The recommendation of MLE as the preferred estimation method emphasizes the xiii importance of methodological choices in statistical inference, providing a valuable contribution to researchers and practitioners across diverse fields.