The present paper discussed the problem of estimating the stress-strength reli- ability parameter R = P(X < Y ), where X and Y follow the Pareto distribution, independently. Assuming X has the Pareto distribution in the presence of outliers and the random variable Y is not contaminated with outliers. Dierent estimators of R were derived when only the shape parameters are unknown. In particular, we obtain the maximum likelihood, moment method and least squares estimator of the unknown parameters and derived estimates of R. Also, in each situation the shrinkage estimation of the stress-strength reliability parameter is derived by using a prior guess R0. Monte Carlo simulation study has been used to compare the dierent methods of estimation in any situation.

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