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

Standard library statistical functions.

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# Logarithm of Cumulative Distribution Function

> [Uniform][uniform-distribution] distribution logarithm of [cumulative distribution function][cdf].

<section class="intro">

The [cumulative distribution function][cdf] for a [continuous uniform][uniform-distribution] random variable is

<!-- <equation class="equation" label="eq:uniform_cdf" align="center" raw="F(x)= \begin{cases} 0 & \text{for }x < a \\ \frac{x-a}{b-a} & \text{for }a \le x < b \\ 1 & \text{for }x \ge b \end{cases}" alt="Cumulative distribution function for a uniform distribution."> -->

<div class="equation" align="center" data-raw-text="F(x)= \begin{cases} 0 &amp; \text{for }x &lt; a \\ \frac{x-a}{b-a} &amp; \text{for }a \le x &lt; b \\ 1 &amp; \text{for }x \ge b \end{cases}" data-equation="eq:uniform_cdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/uniform/logcdf/docs/img/equation_uniform_cdf.svg" alt="Cumulative distribution function for a uniform distribution.">
    <br>
</div>

<!-- </equation> -->

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

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### logcdf( x, a, b )

Evaluates the logarithm of the [cumulative distribution function][cdf] (CDF) for a [uniform][uniform-distribution] distribution with parameters `a` (minimum support) and `b` (maximum support).

```javascript
var y = logcdf( 9.0, 0.0, 10.0 );
// returns ~-0.105

y = logcdf( 0.5, 0.0, 2.0 );
// returns ~-1.386

y = logcdf( -Infinity, 2.0, 4.0 );
// returns -Infinity

y = logcdf( +Infinity, 2.0, 4.0 );
// returns 0.0
```

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

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

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

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

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

```javascript
var y = logcdf( 1.0, 2.5, 2.0 );
// returns NaN
```

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

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

```javascript
var mylogcdf = logcdf.factory( 0.0, 10.0 );
var y = mylogcdf( 0.5 );
// returns ~-2.996

y = mylogcdf( 8.0 );
// returns ~-0.223
```

</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 logcdf = require( '@stdlib/stats/base/dists/uniform/logcdf' );

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 = logcdf( 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">

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

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

</section>

<!-- /.links -->