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

## Description

Simulation of the Thomas model.

## Usage

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

## Arguments

 `pars` a named vector of containing the values of the model parameters (`mu`, `nu`, `sigma`), where `mu` is an intensity of parents, `nu` is an expected number of descendants for each parent and `sigma` is a parameter of the dispersal kernel. `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

Let random variable U be independently and uniformly distributed in [0,1]. We put

U = integral_0^r q_σ(t)dt = 1 - exp(-r^2/(2σ^2)).

Then we have

r = σ √{ -2log(1-U) }.

Each of the offspring coordinates (x_j^i, y_j^i) is given like that of `SimulateIP`.

## 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, sigma = 0.03) SimulateThomas(pars, seed = 117) ```

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