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The resulting algorithm permits simultaneous estimation of the regression parameter, the baseline cumulative hazard, and the parameter indexing a general frailty distribution. We develop novel moment\u2010based estimators for the frailty parameter, including a generalized method of moments estimator. Standard error estimates for all parameters are easily obtained using a randomly weighted bootstrap procedure. For the commonly used gamma frailty distribution, the proposed algorithm is very easy to implement using widely available numerical methods. Simulation results demonstrate that the algorithm performs very well in this setting. We re\u2010analyz several previously analyzed data sets for illustrative purposes. 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