Simulation and Parameter Estimation of Randomized Sierpinski Carpets using the p-p-p-q-Model

Abstract

For data consisting of zeros and ones the parameters p and q are estimated on basis of randomized Sierpinksi Carpets. This is done with the aid of [p,p,p,q]-models. Main function estimationFunction(daten, decs) is called and delivers the two estimates rounded on four decimal places. The estimates are calculated with respect to one ramification step, i.e. the last step for q and the third step for p. The function "createsmallerMatrix" enables to calculate the "underlying" matrix on basis of the main matrix. Hence, this computed matrix is filled with special algorithm with values zero respectively one according to numbers of the original data. We also provide functions so simulate Sierpinski-Carpets with either constant or changing parameters of the Bernoulli random variables.