Description Usage Arguments Details Value References Examples

Simulation of the Inverse-power type model.

1 | ```
SimulateIP(pars, seed = NULL, plot = TRUE)
``` |

`pars` |
a named vector of containing the values of the model parameters
( |

`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 |

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

For all *r>=0*,

*
Q_{p,c}(r) := integral_0^r q_{p,c}(t)dt*

*
= c^{p-1} (p-1) {(r+c)^{1-p} - c^{1-p}}/(1-p)*

*
= 1 - c^{p-1} (r+c)^{1-p}.*

Here, we put *Q_{p,c}(r) = U*. From this, we have

*
r = c {(1-U)^{1/(1-p)} - 1}.*

Let *(x_i^p, y_i^p), i=1,2,…, I* be a coordinate of each parent point
where the integer *I* is generated from the Poisson random variable
*Poisson(μ)* with mean *μ* from now on. Then, for each *i*,
the number of offspring *J_i* is generated by the random variable
*Poisson(ν)* with mean *ν*. Then, using series of different
uniform random numbers *{U}* for different *i* and *j*,
each of the offspring coordinates *(x_j^i, y_j^i), j=1,2,…,J_i* is
given by

*
x_j^i = x_i^p + r cos(2πU),*

*
y_j^i = y_i^p + r sin(2πU),*

owing to the isotropy condition of the distribution.

Given a positive number *ν* and let a sequence of a random variable
*{Uk}* be independently and uniformly distributed in [0,1],
the Poisson random number *M* is the smallest integer such that

*∑_{k=1}^{M+1} - log Uk > ν,*

where *log* represents natural logarithm.

`parents` |
a list containing two components named " |

`offspring` |
a list containing two components named " |

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.

1 2 | ```
pars <- c(mu = 50.0, nu = 30.0, p = 1.5, c = 0.005)
SimulateIP(pars, seed = 353)
``` |

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

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