# Continuous CDF (Student t) (G Dataflow)

Version:

Computes the continuous Student's t cumulative distribution function (CDF) or the probability that a Student's t-distributed variate takes on a value less than or equal to the quantile of the variate.

## x

Quantile of the continuous random variate.

Default: 1

## k

Number of degrees of freedom.

This input must be greater than 0

Default: 1

## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error

## cdf(x)

Cumulative probability that the continuous random variate has a value less than or equal to x.

## 1-cdf(x)

Cumulative probability that the continuous random variate has a value greater than x.

## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error
If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## Algorithm Definition for the Continuous CDF of a Student's T-Distributed Variate

The following equation defines the continuous CDF of a Student's t-distributed variate.

$cdf\left(x\right)={\int }_{-\infty }^{x}pdf\left(x\right)dx$
$pdf\left(x\right)=\frac{\left\{\mathrm{\Gamma }\left[\left(k+1\right)/2\right]\right\}}{{\left(\pi k\right)}^{1/2}\mathrm{\Gamma }\left(k/2\right){\left[1+\left({x}^{2}/k\right)\right]}^{\left(k+1\right)/2}}$

where

• x is the quantile of the continuous random variate
• k is the degrees of freedom of the variate
• $\mathrm{\Gamma }\left[\left(k+1\right)/2\right]$ is the gamma function with argument (k + 1) / 2

Where This Node Can Run:

Desktop OS: Windows

FPGA: This product does not support FPGA devices