A new Maxwell-Log logistic distribution and its applications for mortality rate data

Abstract

In this research, we extended the Log-Logistic distribution by incorporating it into the Maxwell generalized class, resulting in the Maxwell-Log Logistic (Max-LL ) distribution. The probability density function and cumulative distribution function of the proposed distribution have been defined. The proposed distribution’s density shapes can be left or right-skewed and symmetric. The failure function of this distribution might be increasing, decreasing, or inverted bathtub forms. We discussed some essential properties of the Max-LL distribution, including moments, moment generating function, probability weighted moments, stress-strength, and order statistics. The efficiency of the model parameters has been evaluated through a simulation study utilizing a quantile function. To assess the proposed distribution’s adaptability, we applied it to two lifetime datasets: global COVID-19 mortality rates (for nations with more than 100,000 cases) and Canadian COVID-19 mortality rates. The Maxwell-Log Logistic distribution outperformed other distributions on both datasets, as evidenced by several accuracy measures. This shows that the proposed distribution is the best fit for COVID-19 mortality rate data in Canada and around the world.

Keywords

• Log-Logistic distribution
• Maxwell generalized family
• Maxwell-Log Logistic distribution
• Order statistics
• COVID-19