NScluster (version 1.1.0)

SimplexTypeA: Parameter estimation of Type A model

Description

Parameter estimation of type A model via numerical calculation of the Ripley's K-function.

Usage

SimplexTypeA(offspring, pa, ty=1, x2, skip=1, eps=0.1e-2, process=0, plot=TRUE)

Arguments

offspring

the list of coordinates $(x,y)$ of offspring points.

pa

the initial guesses of the parameters $(mu, nu, a, sigma_1, sigma_2)$.

ty

the variable $Ty$ for the standardized coordinates of points in the rectangular region $[0,1]*[0,Ty]$ without loss of generality except for the scaling.

x2

upper limit value in place of $infty$ in the integral in the distribution function.

skip

the variable for the fast likelihood but rough approximation of the initial estimates. The skip calculate the Palm intensity function in the log-likelihood unction for every skip-th $r_ij$ in the ordered distances of the pairs $i$ and $j$.

eps

the optimization procedure is iterated at most 1000 times until stderr becomes smaller than eps.

process

repot the process of minimizing. Allowed values are

0 :

no report.

1 :

output the process of minimizing the negative Palm log-likelihood function until the values converge to

the MPLE values for given data.

2 :

output the process of optimizing by the simplex with the normalized parameters depending on pa.

The actual estimates are obtained by the indicated x-values times pa.

plot

plot the process of optimizing by the simplex with the normalized parameters depending on pa.

Value

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

  ## simulation
  seeds <- c(822, 913, 905)
  mu <- 50;  nu <- 30;  a <- 0.3;  sig1 <- 0.005;  sig2 <- 0.1
  z <- SimulateTypeA(seeds, c(mu,nu,a,sig1,sig2), pmax=100, omax=150)

  ## Not run: 
#     ## estimation
#     ## need very long c.p.u time in the minimization procedure
#     setOmpNumThreads(2)
#     SimplexTypeA(z$offspring, c(mu,nu,a,sig1,sig2), x2=0.3, skip=1000, process=3)
#   ## End(Not run)