Editing Binomial distribution (section)

== Computational methods ==
=== Random number generation ===
{{further|Pseudo-random number sampling}}
Methods for [[random number generation]] where the [[marginal distribution]] is a binomial distribution are well-established.<ref>Devroye, Luc (1986) ''Non-Uniform Random Variate Generation'', New York: Springer-Verlag. (See especially [http://luc.devroye.org/chapter_ten.pdf Chapter X, Discrete Univariate Distributions])</ref><ref>
{{cite journal
 | pages = 216–222
 | year = 1988
 | doi = 10.1145/42372.42381
 | last2 =  Schmeiser| first1 = V.
 | volume = 31| first2 = B. W.
 | journal = Communications of the ACM
 | title = Binomial random variate generation
 | last1 = Kachitvichyanukul| issue = 2
 | s2cid = 18698828
}}</ref>
One way to generate [[random variate]]s samples from a binomial distribution is to use an inversion algorithm. To do so, one must calculate the probability that {{math|1=Pr(''X'' = ''k'')}} for all values {{mvar|k}} from {{math|0}} through {{mvar|n}}. (These probabilities should sum to a value close to one, in order to encompass the entire sample space.) Then by using a [[pseudorandom number generator]] to generate samples uniformly between 0 and 1, one can transform the calculated samples into discrete numbers by using the probabilities calculated in the first step.