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This book is interested in finding and estimating the death density function,survival probability function and hazard function for three estimation methods(maximum likelihood method,rank set sampling method and shrinkage method)for sample of observation from real data which described the duration of survival for patients who suffer from Leukemia disease based on diagnosis of disease or the enterance of patients to Baghdad general hospital for period(1-4-2012)until(31-12-2012). Before finding these functions probabilistic estimate was derived for the three parameters of this distribution based on complete data using six methods(Maximum likelihood method,Ordinary least squares method,Rank set sampling method,Standard Bayes method,Lindley approximation method and Shrinkage method)for all observations of real data.Finally,comparing the numerical results of three estimation methods(maximum likelihood method,rank set sampling method and shrinkage method)for survival probability function by using Mean squares error and Mean absolute percentage error measures we found that shrinkage estimator method gave us better estimation to the parameters in this distribution for all other estimation.