A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science in Statistics, University of Regina. vii, 49 p. In this study, two estimators of the parameter p of the discrete Laplace distribution DL(p) are considered. The classical method of moments estimator(MME) was derived, and the asymptotic normality of its distribution proved by applying the delta method and juxtaposed with the maximum likelihood estimator(MLE). The accuracy and the asymptotic normality of both estimators were probed using simulation studies. The results of the comparison showed that the estimators were normally distributed when the sample size was large for all values of p. It was also revealed that the MLE was efficient for all scenarios considered. The MME was efficient at all values of p for large sample sizes; however, for small sample sizes, MME was efficient for extreme parameter values. Student yes