The .NET library (formerly called .NET Core) doesn't have built-in functions for classical statistics analyses. But it is possible to implement such functions from scratch. This article presents C# ...

A new asymptotic expansion is derived for the incomplete beta function I(a, b, x), which is suitable for large a, small b and $x > 0.5$. This expansion is of the form ...

We define the incomplete gamma function ratio for positive N by \begin{align*}\tag{1}P(N, b, X) &= \int^X_0 t^{N-1}e^{-bt} dt/ \int^\infty_0 t^{N-1}e^{-bt} dt ...