Analysis of the chaotic maps generating different statistical distributions

The analysis of the chaotic maps, enabling the derivation of numbers from given statistical distributions was presented. The analyzed chaotic maps are in the form x_k+1 = F⁻¹(U(F(x_k))), where F is the cumulative distribution function, U is the skew tent map and F^-1 is the inverse function of F. The analysis was presented on the example of chaotic map with the standard normal distribution in view of his computational efficiency and accuracy. On the grounds of the conducted analysis, it should be indicated that the method not always allows to generate the values from the given distribution. (paper)