In this thesis, new generalized families of distributions namely, Weibull Odd Burr III-G (WOBIII-G), Ristic-Balakhrishnan Odd Burr III-G (RBOBIII-G), Risti ´ c-´ Balakhrishnan Marshall-Olkin-G (RBMO-G), Exponentiated Half-Logistc Odd Burr III-G (EHL-OBIII-G) and Half-Logistic Odd Power Generalized Weibull-G (HLOPGW G) families of distributions are developed and studied in detail. Furthermore, the mathematical and statistical properties of these new families of distributions such as moments and moment generating functions, order statistics, probability weighted moments, stochastic ordering and Renyi entropy are derived and studied in detail. ´ We use some of the existing known baseline models to generate some special cases for these newly generated families of distributions. The maximum likelihood estimation technique is used to estimate model parameters and simulation experiments are conducted to illustrate the consistency of maximum likelihood estimates. Finally we demonstrate the efficacy and flexibility for some of the special cases under these distributions by fitting them to some real data sets. The proposed models presents better fits than other existing equal parameter models.