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# Logarithm of Cumulative Distribution Function

> [Geometric][geometric-distribution] distribution logarithm of [cumulative distribution function][cdf].

<section class="intro">

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

<!-- <equation class="equation" label="eq:geometric_cdf" align="center" raw="F(x;p)= \begin{cases} 0 & \text{ for } x < 0 \\ 1-(1 - p)^{\left\lfloor x \right\rfloor+1} & \text{ otherwise} \end{cases}" alt="Cumulative distribution function for a geometric distribution."> -->

<div class="equation" align="center" data-raw-text="F(x;p)= \begin{cases} 0 &amp; \text{ for } x &lt; 0 \\ 1-(1 - p)^{\left\lfloor x \right\rfloor+1} &amp; \text{ otherwise} \end{cases}" data-equation="eq:geometric_cdf">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/stats/base/dists/geometric/logcdf/docs/img/equation_geometric_cdf.svg" alt="Cumulative distribution function for a geometric distribution.">
    <br>
</div>

<!-- </equation> -->

where `0 <= p <= 1` is the success probability. `x` denotes the number of _failures_ before the first success.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### logcdf( x, p )

Evaluates the logarithm of the [cumulative distribution function][cdf] for a [geometric][geometric-distribution] distribution with success probability `p`.

```javascript
var y = logcdf( 2.0, 0.5 );
// returns ~-0.134

y = logcdf( 2.0, 0.1 );
// returns ~-1.306
```

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

```javascript
var y = logcdf( NaN, 0.5 );
// returns NaN

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

If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.

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

y = logcdf( 2.0, 1.5 );
// returns NaN
```

#### logcdf.factory( p )

Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of a [geometric][geometric-distribution] distribution with success probability `p`

```javascript
var mylogcdf = logcdf.factory( 0.5 );
var y = mylogcdf( 3.0 );
// returns ~-0.065

y = mylogcdf( 1.0 );
// returns ~-0.288
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   In virtually all cases, using the `logpmf` or `logcdf` functions is preferable to manually computing the logarithm of the `pmf` 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/geometric/logcdf' );

var p;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 5.0;
    p = randu();
    y = logcdf( x, p );
    console.log( 'x: %d, p: %d, ln(F(x;p)): %d', x.toFixed( 4 ), p.toFixed( 4 ), y.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

<section class="links">

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

[geometric-distribution]: https://en.wikipedia.org/wiki/Geometric_distribution

</section>

<!-- /.links -->
