New version of Log-Logistic distribution: properties and applications to survival time and demographic data

This paper proposes a Deflation-Inflation Log-Logistic (DILLog) distribution as a sub-model of the Deflation-Inflation Distributed (DID) family, introduced by Alodat and Al-Rawwash (2021). The proposed model offers greater flexibility than the original model in fitting data from real-world problems, especially for survival times and demographic data. The DILLog model is characterized by unimodal right-tailed density and hazard rate functions, and its key statistical properties, including the cumulative distribution function and a closed-form quantile function,are derived. To test the performance of the distribution, a simulation study has been used as well as an application to two real data sets: the age at menarche of Nepalese girls and the survival times of patients suffering from melanoma disease. To illustrate the usefulness and application of the proposed distribution, its parameters were estimated by using the maximum likelihood estimation method. The analysis and plots of the fitted results attest to the the DILLog model being flexible enough to fit the right-skewed real data. The actual application of demographic and survival datasets demonstrates that the DILLog distribution outperforms comparative models.