In this project, I propose an efficient estimation strategy using the idea of pretest and shrinkage estimation for the logistics and exponential distribution based on new sampling techniques when prior non-sample information about the parameter is available. The maximum likelihood estimators (MLEs)  of the parameters of interest were derived for both distributions, and the pretest, shrinkage, and the shrinkage pretest estimators were obtained. The set of estimators was compared via their mean squared errors (MSEs) with respect to the MLE using simulated data generated from both distributions based on a simple random sample(SRS), a sample of first-order statistics, and a sample of maximum order statistics using the same size in all cases. Our results showed the superiority of the sampling techniques over the SRS as well as the pretest and shrinkage pretest estimators over the classical MLE.