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We consider the problem of evaluating the cumulative distribution function(CDF) of the sum of order statistics, which serves to compute outageprobability (OP) values at the output of generalized selection combiningreceivers. Generally, closed-form expressions of the CDF of the sum of orderstatistics are unavailable for many practical distributions. Moreover, thenaive Monte Carlo (MC) method requires a substantial computational effort whenthe probability of interest is sufficiently small. In the region of small OPvalues, we propose instead two effective variance reduction techniques thatyield a reliable estimate of the CDF with small computing cost. The firstestimator, which can be viewed as an importance sampling estimator, has boundedrelative error under a certain assumption that is shown to hold for most of thechallenging distributions. An improvement of this estimator is then proposedfor the Pareto and the Weibull cases. The second is a conditional MC estimatorthat achieves the bounded relative error property for the Generalized Gammacase and the logarithmic efficiency in the Log-normal case. Finally, theefficiency of these estimators is compared via various numerical experiments.

On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances