Simulation of the generalized Thomas model of type A.
SimulateTypeA(pars, seed = NULL, plot = TRUE)a named vector of containing the values of the model parameters
(mu, nu, a, sigma1, sigma2), where
mu is an intensity of parents, nu is an expected number of
descendants for each parent, a is a mixture parameter, sigma1
and sigma2 are parameters of the dispersal kernel for each component.
a positive integer, which is the seed for a sequence of uniform random numbers. The default seed is based on the current time.
logical. If TRUE (default), simulated parent points and
offspring points are plotted.
a list containing two components named "n" and
"xy" giving the number and the matrix of (x,y) coordinates of
simulated parents points respectively.
a list containing two components named "n" and
"xy" giving the number and the matrix of (x,y) coordinates of
simulated offspring points respectively.
Parents' configuration and numbers of the offspring cluster sizes are generated by the same way as the Thomas model.
Let random variable \(U_k, k=1,2\) be independently and uniformly distributed in [0,1]. Then \(r\) satisfies as follows:
$$r = \sigma_1 \sqrt{-2 \log(1-U_1)}, \quad U_2 \le a ,$$ $$r = \sigma_2 \sqrt{-2 \log(1-U_1)}, \quad \mathrm{otherwise.}$$
Each of the offspring coordinates \((x_j^i, y_j^i)\) is given like that of
SimulateIP. Using series of different uniform random numbers
\(\{ U_1, U_2, U \}\) for different \(i\) and \(j\).
U. Tanaka, Y. Ogata and K. Katsura, Simulation and estimation of the Neyman-Scott type spatial cluster models, Computer Science Monographs No.34, 2008, 1-44. The Institute of Statistical Mathematics.
# NOT RUN {
pars <- c(mu = 50.0, nu = 30.0, a = 0.03, sigma1 = 0.005, sigma2 = 0.1)
SimulateTypeA(pars, seed = 575)
# }
Run the code above in your browser using DataLab