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One of the most frequently considered problems related to the capital market is the appropriate modelling of the distributions of rates of return for specific financial instruments. The results of such modelling are often used as an element of a number of tools and methods used for analyzes, diagnoses and forecasts of specific phenomena occurring on financial markets. An adoption a priori of certain assumptions as to the density function of distribution of return rates, seems to be a highly risky approach. A significant deviation of the actual rates of return from the assumed ones may cause a number of negative consequences, including among others that it may be the basis for questioning the credibility and thus the applicability of a number of techniques, methods and models used for analyzes, diagnoses and forecasts of the capital market. The main objective of the study will be to determine the impact of the change in the optimization criterion when estimating the parameters of the stable distribution, on the probability of obtaining a distribution consistent with the theoretical. In addition, the potential impact on this probability of such factors as the adoption of a specific assumption regarding the method of construction of individual numerical intervals or the inclusion of a specific rate of return will also be examined. #0#

Estimation of the distribution of α-stable return rates of stock market indices based on the criterion of minimization of chi-square statistics