On the Extension of the Burr XII Distribution: Applications and Regression

Abstract

In this paper, we introduce a new four-parameter mixture distribution called the Harmonic Mixture Burr XII distribution. The proposed model can be used to model data which exhibit bimodal shapes or are heavy-tailed. Specific properties like non-central and incomplete moments, quantile function, entropy, mean and median deviation, mean residual life, moment generating function, and stress-strength reliability are derived. Maximum likelihood estimation, ordinary least squares estimation, weighted least squares estimation, Cram\'{e}r-von Mises estimation, and Anderson-Darling estimation methods were used to estimate the parameters of the distribution. Simulation studies was performed to assess the estimators and the maximum likelihood estimation was adjudged the best estimator. Using three sets of lifetime data, the empirical importance of the new distribution was determined. When compared to nine (9) extensions of the Burr XII distribution, it was clear that the proposed distribution fit the data better. Using the proposed model, a log-linear regression model called the log-harmonic mixture Burr XII is proposed.