This thesis introduces two general classes of models for analyzing proportion response variable when the response variable Y can take values between zero and one, inclusive of zero and/or one. The models are inflated GAMLSS model and generalized Tobit GAMLSS model. The inflated GAMLSS model extends the flexibility of beta inflated models by allowing the distribution on (0,1) of the continuous component of the dependent variable to come from any explicit or transformed (i.e. logit or truncated) distribution on (0,1) including highly skewed and/or kurtotic or bimodal distributions. The second proposed general class of model is the generalized Tobit GAMLSS model. The generalized Tobit GAMLSS model relaxes the underlying normal distribution assumption of the latent variable in the Tobit model to a very general class of distribution on the real line. The thesis also provides likelihood inference and diagnostic and model selection tools for these classes of models. Applications of both the models are conducted using different sets of data to check the robustness of the proposed models. The originality of the thesis starts from chapter 4 and in particular chapter 5, 6 and 7 with applications of models in chapter 8, 9 and 10.