Recent news articles concerning an article from The Lancet with fabricated
data indicate
that in the sample containing some 900 or so patients, more than 200 had
the same
birthday. I was curious and tried out the p and q birthday functions but
pbirthday
could not handle 250 coincidences with n = 1000. The calculation of upper
prior
to using uniroot produces NaN,
upper<-min(n^k/(c^(k-1)),1)
I was able to get it to work by using logs, however, as in the following
version
function(n, classes = 365, coincident = 2){
k <- coincident
c <- classes
if (coincident < 2) return(1)
if (coincident > n) return(0)
if (n > classes * (coincident - 1)) return(1)
eps <- 1e-14
if (qbirthday(1 - eps, classes, coincident) <= n)
return(1 - eps)
f <- function(p) qbirthday(p, c, k) - n
lower <- 0
upper <- min( exp( k * log(n) - (k-1) * log(c) ), 1 )
nmin <- uniroot(f, c(lower, upper), tol = eps)
nmin$root
}
Ken
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