# NTTDIST

Returns the Student’s t distribution for the specified parameters.

## Syntax

NTTDIST(

• x,
• N,
• Cumulative

)

#### Parameters

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

## Remarks

• Probability density function is given as:
$f(x)=\frac{\Gamma\left(\frac{N+1}{2}\right)}{\sqrt{\pi N\left(1+\frac{x^2}{N}\right)^{N+1}}\Gamma\left(\frac{N}{2}\right)}$

, where $\Gamma(\cdot)$ is gamma function.

• Cumulative distribution function is given as:
$F(x)=\frac{1}{2}-\frac{1}{2}\left[1-I_{\gamma}\left(\frac{1}{2},\frac{N}{2}\right)\right]\text{sign}(x)$

, where $\gamma=\frac{N_1}{N_1+x^2}$ 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.

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A B
Data Description
5 Value for which you want the distribution
8 Value of parameter N
Formula Description (Result)
=NTTDIST(A2,A3,TRUE) Cumulative distribution function for the terms above
=NTTDIST(A2,A3,FALSE) Probability density function for the terms above