Nothing
#COHN ****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
#COHN
#COHN Expected values of M and S
#COHN
"EMS" <- function(n, r, qmin) {
if(length(qmin) != 1) {
warning("not expecting a vector for qmin, using only the first value")
qmin <- qmin[1]
}
zr <- qnorm(qmin)
Em <- gtmoms(zr,1)
momS2 <- CondMomsChi2(n, r, zr)
alpha <- momS2[1]^2 / momS2[2]
beta <- momS2[2] / momS2[1]
suppressWarnings(Es <- sqrt(beta)*exp( lgamma(alpha+0.5) - lgamma(alpha)))
c(Em[1], Es)
}
#COHN ****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
#COHN
#COHN Covariance matrix of M and S
#COHN
#COHN "VMS" <- function(n,r,qmin){
#COHN E <- sapply(1:2,function(i){gtmoms(qnorm(qmin),i)});
#COHN Es <- EMS(n,r,qmin)[2]
#COHN Es2 <- E[2]-E[1]^2
#COHN V2 <- V(n,r,qmin)
#COHN array(c(
#COHN V2[1,1],
#COHN rep(V2[1,2]/(2*Es),2),
#COHN Es2-(Es)^2
#COHN ),dim=c(2,2))
#COHN }
"VMS" <-
function(n, r, qmin) {
if(length(qmin) != 1) {
warning("not expecting a vector for qmin, using only the first value")
qmin <- qmin[1]
}
E <- sapply(1:2, function(i) gtmoms(qnorm(qmin), i))
Es <- EMS(n, r, qmin)[2]
Es2 <- E[2] - E[1]^2
V2 <- V(n,r,qmin)
array(c(V2[1,1], rep(V2[1,2]/(2*Es),2), Es2-(Es)^2),
dim=c(2,2))
}
#COHN ****|==|====-====|====-====|====-====|====-====|====-====|====-====|==////////
#COHN
#COHN Covariance matrix of M and S^2
#COHN Note that E is vector of expected values of X^k given X>qmin
#COHN
#COHN "V" <- function(n,r,qmin){
#COHN n2 <- n-r
#COHN E<-sapply(1:4,function(i){gtmoms(qnorm(qmin),i)});
#COHN cm <- c(E[1],
#COHN E[2]-E[1]^2,
#COHN E[3]-3*E[2]*E[1]+2*E[1]^3,
#COHN E[4]-4*E[3]*E[1]+6*E[2]*E[1]^2-3*E[1]^4
#COHN )
#COHN array(
#COHN c((E[2] - E[1]^2)/n2,
#COHN rep(
#COHN (E[3] - 3*E[1]*E[2] + 2*E[1]^3)/sqrt(n2*(n2-1))
#COHN ,2),
#COHN (cm[4]-cm[2]^2)/n2 + 2/((n2-1)*n2)*cm[2]^2),
#COHN dim=c(2,2))
#COHN }
"V" <- function(n, r, qmin) {
if(length(qmin) != 1) {
warning("not expecting a vector for qmin, using only the first value")
qmin <- qmin[1]
}
k <- n-r
E <- sapply(1:4, function(i) gtmoms(qnorm(qmin),i) )
cm <- c(E[1],
E[2] - E[1]^2,
E[3] - 3*E[2]*E[1] + 2*E[1]^3,
E[4] - 4*E[3]*E[1] + 6*E[2]*E[1]^2 - 3*E[1]^4)
array( c( cm[2]/k, # streamline because TAC has this without the k already computed
rep( cm[3]/sqrt(k*(k-1)), 2), # streamline because TAC has this without the k already computed
(cm[4] - cm[2]^2)/k + 2/((k-1)*k)*cm[2]^2),
dim=c(2,2))
}
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.