NTFDIST

Returns the f distribution for the specified parameters.

Syntax

NTFDIST(

)

x is the value for which you want the distribution ( $x\geq 0$ ).
N1 is a parameter of the distribution $N_1$ (Positive integer).
N2 is a parameter of the distribution $N_2$ (Positive integer).
Cumulative is a logical value that determines the form of the function. If cumulative is TRUE, NTFDIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

Probability density function is given as:
$f(x)=\frac{\Gamma\left(\frac{N_1+N_2}{2}\right)\left(\frac{N_1}{N_2}\right)^\frac{N_1}{2}x^{\frac{N_1}{2}-1}}{\Gamma\left(\frac{N_1}{2}\right)\Gamma\left(\frac{N_2}{2}\right)\left(1+\frac{N_1}{N_2}x\right)^{\frac{N_1+N_2}{2}}}$

, where $\Gamma(\cdot)$ is gamma function.
Cumulative distribution function is given as:
$F(x)=I_\gamma\left(\frac{N_1}{2},\frac{N_2}{2}\right)$

, where $\gamma=\frac{N_1x}{N_2+N_1x}$ and $I_{x}(\cdot,\cdot)$ is regularized incomplete beta function.

The example may be easier to understand if you copy it to a blank worksheet

Create a blank workbook or worksheet.
Select the example in the Help topic.
Note Do not select the row or column headers.

Selecting an example from Help
Press CTRL+C.
In the worksheet, select cell A1, and press CTRL+V.
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A	B
Data	Description
5	Value for which you want the distribution
4	Value of parameter N1
30	Value of parameter N2
Formula	Description (Result)
=NTFDIST(A2,A3,A4,TRUE)	Cumulative distribution function for the terms above
=NTFDIST(A2,A3,A4,FALSE)	Probability density function for the terms above