Behavior of Goal Programming with Heavy Tailed Distribution

Abstract

Goal programming (GP) is an extension of linear programming (LP). The GP is an important technique for decision makers. Goal programming technique has a useful advantage in minimize the unwanted deviations between the achievement of goals and their aspiration levels. The purpose of regression analysis is to expose the relationship between a response variable and predictor variables. In real applications, the response variable cannot be predicted exactly from the predictor variables. The response for a fixed value of each predictor variable is a random variable. For this reason, the behavior of the response may be summarized for fixed values of the predictors using measures of central tendency. Typical measures of central tendency are the average value (mean), the middle value (median) or the most likely value (mode). The main purpose for this study is to compare between two statistical method and one operation research method when these method used to estimate multiple linear regression equation with heavy tailed distribution. A simulation study based on four performance indexes to evaluate the performance of the three methods. The study suggested root mean square error with respect to the median (RMSEM) to use as a criteria to compare between three methods under consideration. The aim of this study is to study the behavior of goal programming and OLS, ALV to estimate the parameter of simple linear regression.