@stdlib/stats/base/dists/uniform/logpdf/README.md

Standard library statistical functions.

<!--

@license Apache-2.0

Copyright (c) 2018 The Stdlib Authors.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

-->

# 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.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/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 for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<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 -->