The problem of estimating R=P(Y X) , where X and Y are independent random variables, has received a continuous interest. It is referred to as the reliability parameter that one random variable exceeds another. If , then either the component fails or the system that uses the component may malfunction . This problem also arises in situations where X and Y represent lifetimes of two devices and one wants to estimate the probability that one fails befor the other. So R=Pr(Y X) is a measure of component reliability. It has many applications esoecially in electrical, electronic and mechanical systems such as fatigue failure of aircraft structures, and the aging of concrete pressure vessels. It has also some applications in biological, medical and health service research. Balakrishnan and leung defined the generalized logistic (GL) distribution as one of three generalized forms of the standard logistic distribution. Raqab described the Bayesian and empirical Bayesian methods for the stress-strength parameter R=P(Y X) , when X and Y are independent random variable from two generalized logistic (GL) distribution having the same know scale but different shape parameters. In this thesis we discuss different properties of the two generalizations of the logistic distributions . The first generalization is carried out using the basic idea of Azzalini and we call it as the skew logistic distribution and the second generalization we propose as a proportional reversed hazard family with the base line distribution as the logistic distribution. It is also known in the literature as the type-I generalized logistic distribution and then briefly discuss on the Stress-Strength models. In chapter 5, we consider the estimation of R , when X and Y are both two-parameter GL distribution with the same unknown scale but different shape parameter . The maximum likelihood estimator (MLE) of R and its asymptoti c distribution are obtained and it is used to construct the asymptotic confidence interval of R . We also implement Gi and Metropolis sampling to provide a sample-based estimate of R and its associated credible interval . Finally, analyzes of real data set and Monte Carlo simulation are presented for illustrative purposes.