Add random.binomialvariate() #81620

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1. rhettinger commented on Jun 28, 2019

   

   rhettinger

   on Jun 28, 2019

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   This a small snippet of code I written dozens of times. It would be nice to have this in the library along with the other distributions.

   def binomialvariate(n, p):
       ''' Binomial distribution for the number of successes
           in *n* Bernoulli trials each with a probability *p*
           of success.

       Returns an integer in the range:  0 <= X <= n
   '''
   return sum(random() < p for i in range(n))
   
2. rhettinger

   added

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   stdlibStandard Library Python modules in the Lib/ directoryStandard Library Python modules in the Lib/ directory

   type-featureA feature request or enhancementA feature request or enhancement

   on Jun 28, 2019
3. mdickinson commented on Jul 1, 2019

   

   mdickinson

   on Jul 1, 2019

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   If you want to be able to switch to something more efficient for large n, Knuth describes a simple O(log(n)) algorithm in TAOCP volume 4 (and attributes it to J. H. Ahrens). It's essentially a bisection search on the value, using the fact that we can use the beta distribution to generate order statistics. Here's a (too) simple Python implementation. It still needs thorough testing, and could be optimised in many ways - e.g., using sensible crossover point for n and not recursing all the way to n = 0.

       def binomialvariate(n, p):
           if n == 0:
               return 0
           a, b = (1 + n)//2, 1 + n//2
           x = betavariate(a, b)
           if x < p:
               return a + binomialvariate(b - 1, (p - x)/(1 - x))
           else:
               return binomialvariate(a - 1, p/x)

   >>> binomialvariate(10**10, 0.5)
   4999944649
4. avinassh commented on Jul 1, 2019

   

   avinasshmannequin

   on Jul 1, 2019

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   @mark - Newb here and before I could see your reply, I sent a PR cos I thought simple implementation provided by Raymond Hettinger was good enough. Shall I update the PR?

   I will add the tests soon.
5. mdickinson commented on Jul 1, 2019

   

   mdickinson

   on Jul 1, 2019

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   @avi That's Raymond's call, but IMO there's absolutely nothing wrong with getting a reference implementation (with tests, documentation, and all the usual trimmings) in first and then making algorithmic improvements later.

   Thanks for the PR!
6. mdickinson commented on Jul 1, 2019

   

   mdickinson

   on Jul 1, 2019

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   [...] and then making algorithmic improvements later.

   Though thinking about it, there is *one* catch: for the random module, it's nice if reproducibility isn't broken more often than necessary in released versions, so it would be best to do any algorithmic tweaking *before* 3.9.0 is released. But that still gives us some time ...
7. rhettinger commented on Aug 23, 2019

   

   rhettinger

   on Aug 23, 2019

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   [Avi]

   Shall I update the PR?

   Yes, please.
8. zkneupper commented on May 18, 2021

   

   zkneuppermannequin

   on May 18, 2021

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   Is adding random.binomialvariate() still under consideration?

   I would be willing to work on this addition to Lib/random.py, as well as the accompanying tests and docs.

   Should I use the type of algorithm hinted at by Mark on 2019-07-01 17:56?
9. gpshead commented on May 25, 2021

   

   gpshead

   on May 25, 2021

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   A presumed optimal version of this is already available in numpy.

   https://numpy.org/doc/stable/reference/random/generated/numpy.random.Generator.binomial.html

   https://github.com/numpy/numpy/blob/2232a473f8713f532c8164c8cf616f7bd05f54a7/numpy/random/_generator.pyx#L2805
10. gpshead

    added

    3.11only security fixesonly security fixes

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    on May 25, 2021
11. mdickinson commented on May 25, 2021

    

    mdickinson

    on May 25, 2021

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    I think the NumPy implementation may be from here: https://core.ac.uk/download/pdf/11007254.pdf

    (though I'm struggling to find a clear citation in the NumPy source)
12. mdickinson commented on May 25, 2021

    

    mdickinson

    on May 25, 2021

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    Nope, that's the wrong paper. It looks as though this is the right one, but it's hidden behind a paywall: https://dl.acm.org/doi/abs/10.1145/42372.42381
13. ezio-melotti

    transferred this issue fromon Apr 10, 2022
14. rhettinger

    added a commit that references this issue on Jul 13, 2022

    GH-81620: Add random.binomialvariate() (GH-94719)

    ed06ec1
15. rhettinger

    closed this as completedon Jul 13, 2022