Incomplete beta function is defined as

A closely related function is regularized beta function:

Incomplete beta functions are often met in statistics. For example, the cumulative distribution functions of the binomial distribution, F-distribution and Student's distribution could be written by using the incomplete beta function.

Incomplete regularized beta function can be calculated by using the **IncompleteBeta** subroutine. To calculate the values, the algorithm uses series expansion or continued fractions representation (depending on an argument value). Inverse incomplete regularized beta function is calculated by using the **InvIncompleteBeta** subroutine. Inverse function is calculated using dichotomy or Newton's method.

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