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Re: st: large numbers in comb(n,k) function: no success
Thank you, Bill. I've just spoken with a mathematician, he showed me a
similar way you did.
the formula I need is actually:
probability=1- [comb(n-m,k)/comb(n, k)]
so I have useful numbers after the computation. (n=180000, m=2, k=2000)
Inna
William Gould, StataCorp LP schrieb:
Inna Becher <[email protected]> wrote,
I would like to implement a comb(n,k) function. But my Stata does not
allow it because of large n, k-numbers. N=180000 and k=2000. Is there
any other way to do it? I wasn't successful by using exp(lnfactorial(n))
in mata as well.
Maarten buis <[email protected]> replied,
The outcome of comb(180000,2000) is going to be,
ridiculously large (> 8e+307) and it hits the limit of what
can be stored in double precision [...]
Yes, that's right. In fact, the answer is between 1e+4770 and 1e+4771.
comb(n, k) is defined
n!
comb(n, k) = --------- = (n!)/( k! (n-k)! )
k! (n-k)!
Thus,
ln(comb(n,k) = ln( (n!)/( k! (n-k)! ) )
= ln(n!) - ln(k!) - ln(n-k)!
Stata has a lnfactorial() function, so we can plug in and get
. scalar n = 180000
. scalar k = 2000
. display lnfactorial(n) - lnfactorial(k) - lnfactorial(n-k)
10983.753
In log base 10, that 10983.753/ln(10) = 4770.1833. Hence my statement,
the answer is between 1e+4770 and 1e+4771.
1e+4770 is unimagineably big. The number of particles in the observable
universe is estimated to be between 1e+72 and 1e+87, so it would not be
possible to tally 1e+4770.
-- Bill
[email protected]
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