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# Distribution function of the Zeta distribution
dzeta <- function(k,gamma=2.5,approx_cutoff=100)
{
zeta_approx <- sum(sapply(seq_len(approx_cutoff),function(x)1/(x^gamma)))
sapply(k,function(k_i)
{
1/(k_i^gamma * zeta_approx)
})
}
# Quantile function of the Zeta distribution
qzeta <- function(p,maxK,gamma=2.5,approx_cutoff=100)
{
vals <- cumsum(dzeta(seq_len(maxK),gamma,approx_cutoff))
sapply(p,function(p_i)
{
indices <- which(vals > p_i)
if (length(indices) == 0)
return(NA)
else
return(indices[1])
})
}
# Draw random numbers from the Zeta distribution
rzeta <- function(n,maxK,gamma=2.5,approx_cutoff=100)
{
maxP <- cumsum(dzeta(seq_len(maxK),gamma,approx_cutoff))
p <- runif(min=0,max=maxP,n=n)
return(qzeta(p,maxK,gamma,approx_cutoff))
}
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