The Maximum Likelihood Estimation of a Longitudinal Data of Household Income in the Presence of Outlier Densities

Abstract

This work reports on the use of maximum likelihood function and the probability graphical method to estimate the location parameter for a mini-metropolis household income(X) with heterogeneous social-economic composition. The Easy-fit software was used to fit the household income data to suggest the possible probability distribution(s) for the data. Some of the suggested distributions were taken as the functional form of the income’s(X as a r.v) probability distribution and they were empirically solved using the maximum likelihood method of estimation(MLE) in comparison to traditional matching moment estimation(MME). The estimate that is most consistent with the sample data were solved analytically based on the distribution function(s) suggested by easy fit software. We also compared the maximum likelihood estimates of obtained from each distribution functions graphically using R-programming language.