fsml_f_pdf Interface

public interface fsml_f_pdf

Probability density function for the F distribution. $$f(x) = \frac{1}{\mathrm{B}\left(\frac{d_1}{2}, \frac{d_2}{2}\right)} \cdot \left( \frac{d_1}{d_2} \right)^{ \frac{d_1}{2} } \cdot \frac{x^{ \frac{d_1}{2} - 1}}{\left(1 + \frac{d_1}{d_2} x \right)^{ \frac{d_1 + d_2}{2} }}, \quad x > 0$$ where $d_1$ = numerator degrees of freedom, $d_2$ = denominator degrees of freedom and $B$ is the complete beta function. (Uses intrinsic gamma function for beta.)

The F distribution is the distribution of $X = \frac{U_1/d_1}{U_2/d_2}$, where $U_1$ and $U_2$ are are random variables with chi-square distributions with $d_1$ and $d_2$ degrees of freedom, respectively.

Module Procedures