Abstarct: In regression problems, Logistic and Probit models are commonly used for proportional response variable in unit interval (0,1). But when the distribution of proportional response is highly skewed, these two models are not suitable, because their underlying distribution i.e. Logistic and Normal are symmetric, hence a contradiction is made. In this thesis, "Simplex regression" is introduced as an alternative solution. Firstly, Simplex distribution baxsed on mixture inverse Gaussian distribution is introduced. Secondly, Simplex simulation studies are made to assert the capabilities of the distribution. As Simplex regression can be defined on the frxamework of "Dispersion models", we explain it first, thereafter, similar to generalized linear models methods, the regression parameters are estimated in two ways: heterogeneous and homogeneous variance. Modeling the longitudinal data by Simplex regression is the last subject in this note. All models are also evaluated by simulation and real examples.