Duration Diabetes Survival Times Modelling Using Some Extended Lomax Distribution

The precise modeling of survival time in diabetes is essential for accurately estimating the potential lifespan of individuals diagnosed with diabetes. One of the key factors in assessing the potential survival times of diabetes patients in a specific region is the probability distribution of diabetes survival times. Therefore, data on diabetes survival times are necessary to conduct statistical modeling, particularly in determining the most suitable probability distribution. Statistical models are developed to draw conclusions about the probability distribution of diabetic patients at the Mandau Regional General Hospital (RSUD) in Bengkalis Regency, Riau Province. To achieve this, six distributions will be utilized and evaluated to identify the best model for describing diabetes survival times. The primary objective of this research is to identify the most appropriate distribution to represent the survival times of diabetes patients from 50 individuals in the Bengkalis region, using the Lomax (LM) distribution, three parameters modified Lomax distributions (Rayleigh Lomax (RL), Logistics Lomax (LL), New Rayleigh Lomax (NRL)) and four parameters modified Lomax Distribution (Odd Lomax Log Logistics (OL), Novel Extended Power Lomax (PL)). The maximum likelihood method will be employed to estimate the parameter values of the distributions used in this study. Additionally, graphical assessments (density-density plot) and numerical criteria (Akaike’s Information Criterion (AIC), -log likelihood (-l)) will be utilized to determine the best-fitting model. In most instances, the results obtained from graphical assessments were consistent but differed from the numerical criteria. The model with the lowest values of AIC and -l was selected as the best fit. Overall, the RL and OL distributions was identified as the most suitable model.