vii ABSTRACT The Odd Generalized Exponential-Exponential Distribution (OGEED) could be used in various fields to model variables whose chances of success or survival decreases with time. It was also discovered that the OGEED has higher positive skewness and has been found to have performed better than some existing distributions such as the Gamma, Exponentiated Exponential, Weibull and Pareto distributions in a real life applications. The shape parameter of the Odd Generalized Exponential-Exponential Distribution using the Bayesian method of estimation and comparing the estimates with that of maximum Likelihood by assuming two non-informative prior distributions namely; Uniform and Jeffrey prior distributions. These estimates were obtained using the squared error loss function (SELF), Quadratic loss function (QLF) and precautionary loss function (PLF). The posterior distributions of the OGEED were derived and also the Estimates and risks were also obtained using the above mentioned priors and loss functions. Furthermore, we carried out Monte-Carlo simulation using R software to assess the performance of the two methods by making use of the Biases and MSEs of the Estimates under the Bayesian approach and Maximum likelihood method. Our result showed that Bayesian Method using Quadratic Loss Function (QLF) under both Uniform and Jeffrey priors produces the best estimates of the shape parameter compared to estimates using Maximum Likelihood method, Squared Error Loss Function (SELF) and Precautionary Loss Function (PLF) under both Uniform and Jeffrey priors irrespective of the values of the parameters and the different sample sizes. It is also discovered that the scale parameter has no effect on the estimates of the shape parameter.