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Formulas: Cumulative Distribution Function (CDF) for the t-Distribution

Cumulative Distribution Function (CDF) for the t-Distribution Formulas

Below you will find descriptions and details for the 4 formulas that are used to compute cumulative distribution function (CDF) values for Student's t-distribution.

Beta function:
Beta function formula
Lower incomplete beta function:
Lower incomplete beta function formula
Regularized lower incomplete beta function:
Regularized lower incomplete beta function formula
where the numerator is the lower incomplete beta function, and the denominator is the beta function.
t-distribution cumulative distribution function (CDF):
t-distribution cumulative distribution function (CDF) formula
where v is the degrees of freedom, t is the upper limit of integration, and I is the regularized lower incomplete beta function.
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