# NTCHISQDIST

Returns the chi square distribution for the specified parameters.

## Syntax

NTCHISQDIST(

• 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, NTCHISQDIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

## Remarks

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

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

• Cumulative distribution function is given as:
$F(x)=\frac{\Gamma_{\frac{x}{2}}\left(\frac{N}{2}\right)}{\Gamma\left(\frac{N}{2}\right)}$

, where $\Gamma_{x}(\cdot)$ is incomplete gamma 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
A B
Data Description
2 Value for which you want the distribution
9 Value of parameter N
Formula Description (Result)
=NTCHISQDIST(A2,A3,TRUE) Cumulative distribution function for the terms above
=NTCHISQDIST(A2,A3,FALSE) Probability density function for the terms above