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stdrdize_hist <- function(At,quadnodes)
{
weigm <- weighted.mean(quadnodes,At) # compute weighted mean
quadnodesC <- quadnodes - weigm # centering nodes
weigSD <- sqrt(sum((At*(quadnodesC)^2)/sum(At))) # compute weighted sd
quadnodesCS <- quadnodesC/weigSD # scale nodes
At_new <- At *weigSD # rescale weights
DELTA <- quadnodesCS[2] - quadnodesCS[1] # estimate the difference between two adjacent categories
LG <- length(At_new) # number of nodes
expolERG <- sapply(quadnodes,function(x) # extra/interpolate between nodes - see woods article of EH
{
if(x < min(quadnodesCS))
{
eins <- (At_new[1]/At_new[2])^((quadnodesCS[1] - x)/DELTA)
Nq <- eins * At_new[1]
} else if(x > max(quadnodesCS))
{
eins <- (At_new[LG]/At_new[LG-1])^((x - quadnodesCS[LG])/DELTA)
Nq <- eins * At_new[LG]
} else {
drueber <- which(x < quadnodesCS)[1] # gibt mir den darueberliegenden node
drunter <- which(x > quadnodesCS)[length(which(x > quadnodesCS))]
Nq <- (x - quadnodesCS[drunter])/DELTA * (At_new[drueber] - At_new[drunter]) + At_new[drunter]
}
})
# normalize and name
weights <- expolERG / sum(expolERG)
nodes <- quadnodes
return(list(nodes=nodes,weights=weights))
}
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