Incomplete beta function

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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