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#peta <- function(pzr,n,r,eta){
# zr <- qnorm(qbeta(pzr,shape1=r,shape2=n+1-r))
# CV <- VMS(n,r,qmin=pnorm(zr))
# lambda <- CV[1,2]/CV[2,2]
# etap <- eta + lambda
# EMp <- EMS(n,r,qmin=pnorm(zr))
# muMp <- EMp[1]-lambda*EMp[2]
# SigmaMp <- sqrt(CV[1,1] - CV[1,2]^2/CV[2,2]);
# momS2 <- CondMomsChi2(n,r,zr)
# shape <- momS2[1]^2/momS2[2]
# scale <- momS2[2]/momS2[1]
# sqrtS2 <- sqrt(momS2[1])
# df <- 2*shape
# ncp <- (muMp-zr)/SigmaMp
# q <- -(sqrtS2/SigmaMp)*etap
# (1 - pt(q,df=df, ncp=ncp, lower.tail = TRUE))
# }
"peta" <- function(pzr, n, r, eta) {
sapply(pzr, function(the.pzr) {
br <- qbeta(the.pzr, shape1=r, shape2=n+1-r) # isolated by WHA
zr <- qnorm(br) # so that br can be used twice without need for pnorm().
COV <- VMS(n, r, qmin=br)
EMp <- EMS(n, r, qmin=br)
lambda <- COV[1,2] / COV[2,2] # renamed to be more COVariance like
etap <- eta + lambda
muMp <- EMp[1] - lambda*EMp[2]
suppressWarnings(SigmaMp <- sqrt(COV[1,1] - COV[1,2]^2/COV[2,2])) # WHA error trapping
if(! is.finite(SigmaMp)) return(1) # TODO, Is unity okay? Seems so # WHA error trapping
momS2 <- CondMomsChi2(n,r,zr)
# shape <- momS2[1]^2/momS2[2] # WHA: only needed for df
# scale <- momS2[2] / momS2[1] # WHA: not used by TAC
q <- -(sqrt(momS2[1]) / SigmaMp)*etap # a quantile for pt()
df <- 2*(momS2[1]^2 / momS2[2]) # degrees of freedom
ncp <- (muMp-zr) / SigmaMp # non-centrality parameter
#if(abs(ncp) > 37.62) { # WHA limit exploring of pt(), 37.62 from R documentation
# message("Exploring limits of peta:",q, ", df=",df," and ncp"=ncp)
#}
suppressWarnings(the.pt <- pt(q, df=df, ncp=ncp, lower.tail=TRUE))
return(1 - the.pt)
})
}
# Peaks <- c(53, 88, 55, 45, 40); MGBT(Peaks)
# if(! is.finite(SigmaMp)) return(1)
#$pvalues for 40 and 45
#[1] 0.8139058 0.8011052
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