FractalParameterEstimation (version 1.1.2)

GSC_seq: 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.

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

# NOT RUN {
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. 
# }