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#takes in marginal cdf evals (u1 u2) and joint copula eval to impose bounds
frech.bounds = function(u1, u2, p, frech.min = 1e-7) {
fmax = 1 - frech.min
low = pmax(u1 + u2 - 1, frech.min)
up = if(frech.min > 0) pmin(u1, u2, fmax) else pmin(u1, u2)
out = pmin( pmax(p, low), up)
return(out)
}
bound = function(x, low=1e-7, upper=T){
if(low >= 1 || low <= 0)
stop("Invalid lower boundary.")
up = 1-low
v = if(!upper)
pmax(low, x)
else
pmin(up, pmax(low, x))
return(v)
}
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