From: Lavan <rsumithran_at_yahoo.com>

Date: Mon, 24 Mar 2008 20:05:18 -0700 (PDT)

(c(n*(x_bar-mu[i,j])/(sigma^2)-(t1[i]-a1)/(tau1^2),n*(x_bar-mu[i,j])/

(sigma^2)-(t2[j]-a2)/(tau2^2)));

}

Date: Mon, 24 Mar 2008 20:05:18 -0700 (PDT)

hi thanks,

pls see the code below. the elements of matrix Il should be the derivatives
in matrix h (in Boldface) plus some additional terms, here I did calculate
derivatoves in the matrix, but I want R to calculate it for me.

pid<- function (tau1,tau2,sigma=10,n=100,x_bar=20) {

library(akima) library(lattice) library(rgl) a1 <- 1.5 a2 <- 4 t1 <-seq(-1,1); t2 <-seq(3,4); l <-length(t1); m <-length(t2); N1 <- matrix(NA,l,m); N2 <- matrix(NA,l,m); wp <- matrix(NA,l,m); rr <- matrix(NA,l,m); N <- matrix(NA,l,m); mu <- matrix(NA,l,m); Il <- matrix(NA,l,m); iIl <- matrix(NA,l,m); theta <-expression(x+y); dx <-D(theta, "x"); dy <-D(theta, "y"); d2x <-D(dx, "x"); dxy <-D(dx, "y"); dyx <-D(dy, "x"); d2y <-D(dy, "y"); h <- matrix(c(d2x,dxy,dyx,d2y),nrow=2,ncol=2); for (i in 1:l) { for (j in 1:m) { wp[i,j]<-((t1[i]-a1)/tau1)^2+((t2[j]-a2)/tau2)^2 mu[i,j] <-(t1[i] + t2[j]); Il[i,j] <-matrix(c(n/(sigma^2)+1/(tau1^2),n/(sigma^2),n/(sigma^2),n/(sigma^2)+1/ tau2^2)),2,2); iIl <-solve(Il); ul[i,j] <-

(c(n*(x_bar-mu[i,j])/(sigma^2)-(t1[i]-a1)/(tau1^2),n*(x_bar-mu[i,j])/

(sigma^2)-(t2[j]-a2)/(tau2^2)));

ul <-matrix(c(n*(x_bar-mu)/(sigma^2)-(theta1-a1)/(tau1^2),n*(x_bar-mu)/

(sigma^2)-(theta2-a2)/(tau2^2)),2,1);

ult <-t(ul); wl[i,j] <-t(ul)%*%solve(Il,ul); rr[i,j] <-(wp[i,j]/wl[i,j]); N[i,j] <-(wl[i,j]-wp[i,j])/wl[i,j] }

}

list("Test Statistics Wp"= wp,"Stat Ratio"=rr, "N"=N,"N1"=N1, "N2"=N2, "mean"=mu, "Il"=Il,

"inverse of Il"=iIl)

}

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