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

Uthumporn  Panitanarak; Aliyu  Ismail Ishaq; Alfred Adewole Abiodun; Hanita  Daud; Ahmad Abubakar Suleiman

doi:10.46481/jnsps.2025.1976

Authors

Uthumporn Panitanarak Department of Biostatistics, Faculty of Public Health, Mahidol University, 10400, Thailand
Aliyu Ismail Ishaq
binishaq05@gmail.com
Department of Statistics, Ahmadu Bello University, Zaria, 810107, Nigeria
Alfred Adewole Abiodun Department of Statistics, University of Ilorin, Ilorin, 240003, Nigeria
Hanita Daud Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar, 32610, Malaysia
Ahmad Abubakar Suleiman Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Seri Iskandar, 32610, Malaysia

Keywords:

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

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.

Dimensions

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