Statistical Inference for Heavy-Tailed Burr X Distribution with Applications

In this article, we present a new distribution, the so-called heavy-tailed Burr X (HTBX) distribution. It comes from the newly discovered heavy-tailed (HT) family of distributions. A notable feature is that the associated probability density function can have a right-skewed distribution that approximates symmetry, unimodality, and decreasing values, which makes it well suited for modeling various datasets. The mathematical properties of the new distribution are obtained by calculating the quantile function, ordinary moments, incomplete moments, moment generating function, conditional moment, mean deviation, Bonferroni curve, and Lorenz curve. Extensive simulation was performed to investigate the estimation of the model parameters using many established approaches, including maximum likelihood estimation, least squares estimation, weighted least squares estimation, Cramer–von Mises estimation, Anderson–Darling estimation, maximum product of spacing estimation, and percentile estimation. The simulation results showed the computational efficiency of these strategies and showed that the maximum likelihood strategy of estimation is the best strategy. The utility and importance of the newly proposed model are demonstrated by analyzing three real datasets. The HTBX distribution is compared to several well-known extensions of the Burr distribution such as exponentiated Kavya-Manoharan Burr X, Kavya-Manoharan Burr X, Burr X, Kumaraswamy Rayleigh, Kumaraswamy Burr III, exponentiated Burr III, Burr III, Kumaraswamy Burr-II, Rayleigh, and HT Rayleigh models by using different measures. The numerical results showed that the HTBX model fit the data better than the other competitive models.