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# PHP | stats_dens_t() Function

Hello folks! welcome back to a new edition of our tutorial on PHP. In this tutorial guide, we are going to be studying about the PHP stats_dens_t() Function.

The built-in stats_dens_t() function is the probability density function of t distribution.

## Syntax

Following below is the syntax to use this function -

`float stats_dens_t( float \$x, float \$dfr )`

## Parameter Details

Sr.NoParameterDescription
1

x

The value at which the probability density is calculated

2

dfr

The degree of freedom of the distribution

## Return Value

This built-in function returns the probability density at x, where the random variable can follow the t distribution of which the degree of freedom is dfr, else false on failure.

## Dependencies

This built-in function was first introduced in statistics extension (PHP version 4.0.0 and PEAR v1.4.0). In this tutorial guide, we used the latest release of stats-2.0.3 (PHP v7.0.0 or newer and PEAR version 1.4.0 or newer).

### Example1

The following example below computes the probability density at x -

```<?php
// check foreach x
foreach (range(-1, 1, 0.5) as \$x) {
var_dump(round(stats_dens_t(\$x, 1), 6));
echo "<br>";
}
?>```

#### Output

When the above code is executed, it will produce the following result -

```float(0.159155)
float(0.254648)
float(0.31831)
float(0.254648)
float(0.159155)```

### Example2

The following example below computes the probability density for each dfr -

```<?php
// check foreach dfr
foreach (range(0.5, 2, 0.5) as \$dfr) {
var_dump(round(stats_dens_t(0, \$dfr), 6));
echo "<br>";
}
?>```

#### Output

When the above code is executed, it will produce the following output -

```float(0.269676)
float(0.31831)
float(0.340735)
float(0.353553)```

### Example3

The following below is an error case. In the below example, we have passed dfr == 0. A warning is shown in logs -

```<?php
// error cases
var_dump(stats_dens_t(1, 0));   // dfr == 0
?>```

#### Output

The above code will produce the following result and a warning in logs PHP Warning: stats_dens_t(): dfr == 0.0

`bool(false)`

Alright guys! This is where we are going to be rounding up for this tutorial post. In our next tutorial, we are going to be discussing about the built-in PHP stats_dens_uniform() Function.

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