Efficient estimation of the density and distribution functions of Weibull-Burr XII distribution

Abstract

This study takes into account the efficient estimation of the probability density function (PDF) of the Weibull-Burr XII distribution and the cumulative distribution function (CDF), which allows for greater flexibility than many other generalized distributions in use today. Nine traditional estimators are used to produce the analytical formulations for the bias and the mean squared error (MSE). A simulated investigation is conducted to evaluate the finite sample performance of the suggested estimators in terms of MSE values. In addition to that a real data application is also demonstrated for illustration.

Keywords

• Weibull-Burr XII distribution
• Maximum likelihood estimator
• Moment estimator
• Uniformly minimum variance unbiased estimator