NTFDIST

Returns the f distribution for the specified parameters.

Syntax

NTFDIST(
    x,
    N1,
    N2,
    Cumulative
)

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.

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.

How to copy an example

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.
To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.

	A	B
1	Data	Description
2	5	Value for which you want the distribution
3	4	Value of parameter N1
4	30	Value of parameter N2
5	Formula	Description (Result)
6	=NTFDIST(A2,A3,A4,TRUE)	Cumulative distribution function for the terms above
7	=NTFDIST(A2,A3,A4,FALSE)	Probability density function for the terms above