Binomial Distribution Cumulative Distribution Function (CDF) Formulas

Binomial Distribution Cumulative Distribution Function (CDF) Formulas

Below you will find descriptions and details for the 4 formulas that are used to compute the CDF (cumulative distribution function) for the binomial distribution.

Beta function:

Cumulative distribution function (CDF) for the binomial distribution:

Variable definitions:
x = number of successes
n = number of trials
p = probability of a successful outcome
I = regularized lower incomplete beta function

Lower incomplete beta function:

Regularized lower incomplete beta function:

Variable definitions:
the numerator = lower incomplete beta function
the denominator = beta function