This study discussed how to estimate the parameters of the Pareto-Lévy distribution—which has been recognized as an alternative for describing actual stock return distributions—in the case of asymmetry. Specifically, the study aimed to determine the location parameter and the scale measure for the asymmetric Pareto-Lévy distribution, and to construct the probability distribution table for the standardized Pareto-Lévy distribution. In addressing these topics, this study estimated the asymmetry of the actual distribution and approached the solution through simulation experiments to explain it. Based on the results of these simulation experiments, a new scale measure accounting for asymmetry was determined to be the median absolute deviation, unlike previous studies. According to this new measurement metric, random numbers were generated from the population of the Pareto-Lévy distribution while varying the characteristic exponent and the asymmetry index, thereby constructing a standardized asymmetric probability distribution table and contributing to research on return distributions.