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# Logarithm of Probability Density Function

> [Uniform][uniform-distribution] distribution logarithm of [probability density function][pdf] (PDF).

<section class="intro">

The [probability density function][pdf] (PDF) for a [continuous uniform][uniform-distribution] random variable is

<!-- <equation class="equation" label="eq:uniform_pdf" align="center" raw="f(x;a,b)=\begin{cases} \frac{1}{b - a} & \text{for } x \in [a,b] \\ 0 & \text{otherwise} \end{cases}" alt="Probability density function (PDF) for a continuous uniform distribution."> -->

<div class="equation" align="center" data-raw-text="f(x;a,b)=\begin{cases} \frac{1}{b - a} &amp; \text{for } x \in [a,b] \\ 0 &amp; \text{otherwise} \end{cases}" data-equation="eq:uniform_pdf">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/stats/base/dists/uniform/logpdf/docs/img/equation_uniform_pdf.svg" alt="Probability density function (PDF) for a continuous uniform distribution.">
    <br>
</div>

<!-- </equation> -->

where `a` is the minimum support and `b` is the maximum support of the distribution. The parameters must satisfy `a < b`.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var logpdf = require( '@stdlib/stats/base/dists/uniform/logpdf' );
```

#### logpdf( x, a, b )

Evaluates the logarithm of the [probability density function][pdf] (PDF) for a [continuous uniform][uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).

```javascript
var y = logpdf( 2.0, 0.0, 4.0 );
// returns ~-1.386

y = logpdf( 5.0, 0.0, 4.0 );
// returns -Infinity

y = logpdf( 0.25, 0.0, 1.0 );
// returns 0.0
```

If provided `NaN` as any argument, the function returns `NaN`.

```javascript
var y = logpdf( NaN, 0.0, 1.0 );
// returns NaN

y = logpdf( 0.0, NaN, 1.0 );
// returns NaN

y = logpdf( 0.0, 0.0, NaN );
// returns NaN
```

If provided `a >= b`, the function returns `NaN`.

```javascript
var y = logpdf( 2.5, 3.0, 2.0 );
// returns NaN

y = logpdf( 2.5, 3.0, 3.0 );
// returns NaN
```

#### logpdf.factory( a, b )

Returns a `function` for evaluating the logarithm of the [PDF][pdf] of a [continuous uniform][uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).

```javascript
var mylogPDF = logpdf.factory( 6.0, 7.0 );
var y = mylogPDF( 7.0 );
// returns 0.0

y = mylogPDF( 5.0 );
// returns -Infinity
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/stats/base/dists/uniform/logpdf' );

var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 25; i++ ) {
    x = (randu() * 20.0) - 10.0;
    a = (randu() * 20.0) - 20.0;
    b = a + (randu() * 40.0);
    y = logpdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, ln(f(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

<section class="links">

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

[uniform-distribution]: https://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29

</section>

<!-- /.links -->
