GSC_seq {FractalParameterEstimation}

Simulation of Random Sierpinski-Carpets using variable probabilities

Description

This function simulates random Sierpinski-Carpets using different probabilities per ramification for the computation of the Bernoulli random variables placed in the matrix.

Usage

GSC_seq(p, sierp=TRUE)

Arguments

p

A numeric vector of same length as ramifications for the simulated Sierpinski-Carpet. The vector contains values between 0 and 1 indicating the probability of success (0 or 1) for the Bernoulli random variables of the matrix in each ramification step.

sierp

An optional logical parameter: if TRUE then the center of the matrix is automatically set to 0 as for the general Sierpinski-Carpet, else also a Bernoulli random variable is simulated.

Value

This function creates a matrix of size 3^N x 3^N containing simulated zeros and ones from Bernoulli distribution under given probability p. Here, N is the ramification which equals the length of the input vector p.

Author(s)

Philipp Hermann; Jozef Kiselak; Milan Stehlik\ [e-mail]; [e-mail]; [e-mail]

References

Hermann, P., Mrkvicka, T., Mattfeldt, T., Minarova, M., Helisova, K., Nicolis, O., Wartner, F., and Stehlik, M. (2015). Fractal and stochastic Geometry Inference for Breast Cancer: a Case Study with Random Fractal Models and Quermass-Interaction Process. Statistics in Medicine, 34(18), 2636-2661. doi: 10.1002/sim.6497.

Examples

GSC_seq(p = c(0.1,0.2,0.1,0.4), sierp = TRUE)
GSC_seq(p = c(rep(0.1,3),0.05), sierp = FALSE)  
## this example equals th pppq-model for the estimation.