NTFDIST

Returns the f distribution for the specified parameters.

Syntax

NTFDIST(

• x,
• N1,
• N2,
• Cumulative

)

Parameters

• 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.

Remarks

• 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.

Example

• The example may be easier to understand if you copy it to a blank worksheet
How to copy an example
1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

Note  Do not select the row or column headers.

Selecting an example from Help

3. Press CTRL+C.
4. In the worksheet, select cell A1, and press CTRL+V.
5. 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.

1
2
3
4
5
6
7
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