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NTCHIDIST

Returns the chi distribution for the specified parameters.

Syntax

NTCHIDIST(

x,
N,
Cumulative

)

Parameters

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

Remarks

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

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

, 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

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.


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

Download sample excel sheet

See also

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