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From |
wgould@stata.com (William Gould, StataCorp LP) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: large numbers in comb(n,k) function: no success |

Date |
Thu, 05 Feb 2009 09:13:33 -0600 |

Inna Becher <inna.becher@uni-konstanz.de> 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 <maartenbuis@yahoo.co.uk> 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 wgould@stata.com * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: large numbers in comb(n,k) function: no success***From:*Inna Becher <inna.becher@uni-konstanz.de>

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