likelihood function

Modeling is one of the most basic methods to explain the statistical variables that by using it we can realize the response variable distribution. Mixture distribution can improve the goodness of fit largely, so, the aim of this study was to introduce the mixture of logarithmic series distribution and modeling of effects of nutrition on complications in diabetic patients by it. This study examined appropriate model fitted related to diabetic patient's data after introducing the mixture of logarithmic series distribution. 32 variables have been considered which related to type and consumption instruction of food as independent variables and complication as dependent variable. The results showed that according to chi-square value of Mixture logarithmic series distribution, fitted model with a mixing ratio of 1/32 to all independent variables are reasonable model.Discussion & given that data of diabetic patient's complications have no zero density and also comparing χ^2 statistic from mixture of logarithmic series distribution combined and mixed Poisson distribution, we find that mixed logarithmic series distribution model gives a better fit to data.