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| | + | #REDIRECT[[Binomial distribution#CumBinomialInv]] |
| | [[Category: Analytic Distribution Functions]] | | [[Category: Analytic Distribution Functions]] |
| | [[Category: Distribution Densities library functions]] | | [[Category: Distribution Densities library functions]] |
| − | | + | [[category:Inverse cumulative probability functions]] |
| − | == CumBinomialInv(u, n, p) ==
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| − | Computes the inverse cumulative probability for the binomial distribution, [[Binomial]](n, p). Returns the greatest number ''k'' such that the probability of seeing ''k'' or fewer successes among «n» independent trials, each individual trial having a success probability of «p», is less than or equal to «u». The result is a number between 0 and «n» inclusive.
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| − | '''Parameters:'''
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| − | * «u» : The overall probability of ''k'' successes in «n» trials (where ''k'' is the result). This is also known as the fractile or quartile level of the outcome. Must be ''0 ≤ «u» ≤ 1''.
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| − | * «n» : The number of trials.
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| − | * «p» : The probability of success for each individual trial. ''0 ≤ «p» ≤ 1''
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| − | Notice that there are two probabilities here, «u» and «p». You need to keep these straight. These are the probability across all trials («u») and the probability for each individual trial («p»).
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| − | == Library ==
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| − | [[Distribution Densities Library]] ([[media:Distribution Densities.ana|Distribution Densities.ana]])
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| − | This function was included in the [[Distribution Densities Library]] for the first time with the Analytica 4.4.3 release. The function itself, however, should work fine in earlier 4.x releases of Analytica.
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| − | == Examples ==
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| − | An experiment is to be conducted that will consist of rolling a die 100 times and counting the number of times a 6 is rolled. With a 75% probability, the number of sixes that will be observe will be less than or equal to:
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| − | :<code>CumBinomialInv(75%, 100, 1/6 )</code>
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| − | [[CumBinomialInv]] is the inverse of [[CumBinomial]], so that for all ''«n» ≥ 0, 0 ≤ k≤ «n»'', and ''0 < «p» < 1'', the following holds (up to the available numeric precision):
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| − | :<code>CumBinomialInv(CumBinomial(k, n, p), n, p) → k</code>
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| − | == Excel equivalent ==
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| − | Excel has two functions that are equivalent to [[CumBinomialInv]]: CRITBINOM(p, n, u) and BINOM.INV(p, n, u). Apparently CRITBINOM is deprecated, and BINOM.INV is the more modern. Just note that the first and third parameters are swapped in Excel vs. [[CumBinomialInv]]. The convention among Analytica's '''Cum''Distribution''Inv''' functions is for the first parameter to be the fractile level, and then for the remaining parameters to be the distribution parameter(s).
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| − | ==History==
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| − | This function was included in the [[media:Distribution Densities.ana|Distribution Densities.ana]] for the first time with the Analytica 4.4.3 release. The function itself, however, should work fine in earlier 4.x releases of Analytica.
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| − | == See Also ==
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| − | * [[CumBinomial]] --- the CDF function for the Binomial distribution
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| − | * [[Prob_Binomial]] --- the probability function for the Binomial distribution
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| − | * [[Binomial]] -- The binomial distribution function
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| − | * [[CumNormalInv]]
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| − | * [[media:Distribution Densities.ana|Distribution Densities.ana]]
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