ESTIMATING COMMON PARAMETERS OF DIFFERENT CONTINUOUS DISTRIBUTIONS

Abstract

Estimating a common parameter is the most essential and quite fascinating task across various probability distributions. This article addresses the challenge of estimating this parameter through the application of Maximum Likelihood Estimation (MLE). Numeric determination of common parameters is conducted for several distributions, including the Lomax distribution, Gamma distribution, Rayleigh distribution, and Weibull distribution. In cases where distributions lack a closed-form solution, estimation of MLEs is achieved using the Newton-Raphson technique. Furthermore, asymptotic confidence intervals are computed utilizing the Fisher information matrix tailored to each distribution. The performance evaluation of these estimators centers on the assessment of bias and mean squared error. To enable a numerical comparison of these estimators, the Monte Carlo simulation method is employed. Finally, these techniques are applied to real-time rainfall data to assess parameter estimates for each distribution.

Keywords

• maximum likelihood estimation
• confidence interval
• gamma distribution
• weibull distribution
• rayleigh distribution
• lomax distribution