We reviewed the generalized family of distributions called the Marshall-Olkin-G Power Series (MO-GPS) family of distributions. Some special models of the MO- GPS family of distributions are reviewed in detail. Some structural statistical properties inclusive of moments, residual and reverse residual life function, stress - strength function, mean deviations, distribution of the order statistics and R´enyi entropy are reviewed for the MO-GPS and its special models. Different estimation techniques are discussed, however the maximum likelihood estimation method is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators was carried out. We model censored and complete data using the MO-GPS family of distributions.

Thesis (MSc of Mathematics and Statistical sciences)---Botswana International University of Science and Technology, 2023