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A special case of the well known T – X family of distributions proposed by Ayman Alzaatreh et al. (2012) called Pareto – Rayleigh (P – R) distribution is considered. Its scale parameter is estimated using a single order statistic in small samples. Optimal criterion for the choice of single order statistic in a given small sample is worked out. Comparison is made with the corresponding optimal choice of single order statistic with respect to the criterion of asymptotic variance. The results are extended to estimate parametric functions like reliability and hazard rate. Keywords: T-X family, Pareto-Rayleigh distribution, order statistics, optimal estimation, asymptotic variance.