Stieltjes Sample Characteristic Function: Singular Continuous Distributions Parameters Estimation

In this paper, the Steiltjes sample characteristic function is introduced and studied. It is applied to establish a new parameter estimation method. The method is useful to estimate parameters of singular continuous distributions, where other estimation procedures such as maximum likelihood and empirical characteristic function fail to be applied. We fit well the Cantor's type distribution with the parameters estimated by the proposed method on the log returns of the daily price of Brazilian coffee. Effectiveness of the estimation approach is also numerically demonstrated in estimating the parameters of the standard two-sided power and the asymmetric Laplace distributions, using simulated and a real financial data set. Certain theoretical derivations concerning the Stieltjes sample characteristic function are given as well.