# SimulateTypeA: Simulation of the Generalized Thomas Model of Type A In NScluster: Simulation and Estimation of the Neyman-Scott Type Spatial Cluster Models

## Description

Simulation of the generalized Thomas model of type A.

## Usage

 `1` ``` SimulateTypeA(pars, seed = NULL, plot = TRUE) ```

## Arguments

 `pars` 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. `seed` a positive integer, which is the seed for a sequence of uniform random numbers. The default seed is based on the current time. `plot` logical. If `TRUE` (default), simulated parent points and offspring points are plotted.

## Details

Parents' configuration and numbers of the offspring cluster sizes are generated by the same way as the Thomas model.

Let random variable Uk, k=1,2 be independently and uniformly distributed in [0,1]. Then r satisfies as follows:

r = σ1 √{ -2log(1-U1) }, U2 <= a ,

r = σ2 √{ -2log(1-U1) }, 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 {U1, U2, U} for different i and j.

## Value

 `parents` a list containing two components named "`n`" and "`xy`" giving the number and the matrix of `(x,y)` coordinates of simulated parents points respectively. `offspring` a list containing two components named "`n`" and "`xy`" giving the number and the matrix of `(x,y)` coordinates of simulated offspring points respectively.

## References

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.

## Examples

 ```1 2``` ```pars <- c(mu = 50.0, nu = 30.0, a = 0.03, sigma1 = 0.005, sigma2 = 0.1) SimulateTypeA(pars, seed = 575) ```

NScluster documentation built on March 19, 2018, 9:03 a.m.