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Cumulative Binomial Probability Calculator
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Cumulative Binomial Probability Calculator
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This calculator will compute cumulative probabilities for a binomial outcome, given the number of successes, the number of trials, and the probability of a successful outcome occurring. For the number of successes x, the calculator will return P(X<x), P(X≤x), P(X>x), and P(X≥x).
Please supply the necessary parameter values, and then click 'Calculate'.
Probability of success:
The probability of a success occurring.
Successes:
The number of successes.
Trials:
The number of trials in the experiment.
Formulas
The following formulas are involved in the calculation of cumulative binomial probability values:
Beta function:
Binomial distribution cumulative distribution function (CDF):
where
x
is the number of successes,
n
is the number of trials,
p
is the probability of a successful outcome, and
I
is the regularized lower incomplete beta function.
Lower incomplete beta function:
Regularized lower incomplete beta function:
where the numerator is the lower incomplete beta function, and the denominator is the beta function.
References
The following references can be used to cite this cumulative binomial probability calculator:
Soper, D.S. (2016). Cumulative Binomial Probability Calculator [Software]. Available from http://www.danielsoper.com/statcalc
Abramowitz, M. and Stegun, I.A., eds. (1965). Handbook of Mathematical Functions. New York, NY: Dover.
Keller, G. (2011). Statistics for Management and Economics (9th edition). Mason, OH: South-Western Cengage.
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