THE COMPARISON DURATION DIABETES SURVIVAL TIMES MODELLING USING LINDLEY (LIN), WEIGHTED LINDLEY EXPONENTIAL (WLE), POWER MODIFIED LINDLEY (PML), LINDLEY HALF-CAUCHY (LHC) AND RAYLEIGHT LOMAX (RL) DISTRIBUTIONS

Abstract

Accurate diabetes survival time modeling is critical in estimating diabetes survival time potential for effectively. One of the bases for assessment of diabetes survival times potential for a specified region is the probability distribution of diabetes survival times, therefore diabetes survival times data is needed to produce statistical modeling, especially in determining the best probability distribution. Statistical models are designed to facilitate conclusions about the occurrence probability distribution of diabetic patient in the Mandau Regional General Hospital (RSUD), Bengkalis Regency, Riau Province. For this purpose, five distributions will be used and tested to determine the best model to describe diabetes survival times. The main goal of this study is to find the best fitting distribution to the duration survival times diabetes of 50 patients measured over Bengkalis region by using lindley (LIN) distribution, three modified lindley distributions such as weighted Lindley exponential (WLE), Power Modified Lindley (PML), Lindley half-Cauchy (LHC) and Rayleight Lomax distribution (RL). The maximum likelihood method will be used to get the estimated parameter value from the distribution used in this study. Furthermore, the graphical inspection (density-density plot and cumulative plot) and numerical criteria (Akaike’s information criterion (AIC), Bayesian Information Criteria (BIC), - log likelihood (- l) were used to determine the best fit model. In most cases, the results produced by the graphical inspection were similar, and differed from the numerical criteria . The best fit result was chosen as the distribution with the lowest values of AIC, BIC and - l. In general, the Rayleight Lomax (RL) distribution has been selected as the best model.