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# Logarithm of Probability Mass Function

> [Geometric][geometric-distribution] distribution logarithm of [probability mass function][pmf] (PMF).

<section class="intro">

The [probability mass function][pmf] (PMF) for a [geometric][geometric-distribution] random variable is defined as

<!-- <equation class="equation" label="eq:geometric_pmf" align="center" raw="\Pr(X = x) = \begin{cases}(1-p)^{x}\,p & \text{ for } x=0,1,2,\ldots \\ 0 & \text{ otherwise } \end{cases}" alt="Probability mass function (PMF) for a geometric distribution."> -->

<div class="equation" align="center" data-raw-text="\Pr(X = x) = \begin{cases}(1-p)^{x}\,p &amp; \text{ for } x=0,1,2,\ldots \\ 0 &amp; \text{ otherwise } \end{cases}" data-equation="eq:geometric_pmf">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/stats/base/dists/geometric/logpmf/docs/img/equation_geometric_pmf.svg" alt="Probability mass function (PMF) for a geometric distribution.">
    <br>
</div>

<!-- </equation> -->

where `0 <= p <= 1` is the success probability. The random variable `X` denotes the number of failures until the first success in a sequence of independent Bernoulli trials.

</section>

<!-- /.intro -->

<section class="usage">

## Usage

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

#### logpmf( x, p )

Evaluates the logarithm of the [probability mass function][pmf] (PMF) of a [geometric][geometric-distribution] distribution with success probability `0 <= p <= 1`.

```javascript
var y = logpmf( 4.0, 0.3 );
// returns ~-2.631

y = logpmf( 2.0, 0.7 );
// returns ~-2.765

y = logpmf( -1.0, 0.5 );
// returns -Infinity
```

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

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

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

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

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

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

#### logpmf.factory( p )

Returns a function for evaluating the logarithm of the [probability mass function][pmf] (PMF) of a [geometric][geometric-distribution] distribution with success probability `0 <= p <= 1`.

```javascript
var mylogpmf = logpmf.factory( 0.5 );
var y = mylogpmf( 3.0 );
// returns ~-2.773

y = mylogpmf( 1.0 );
// returns ~-1.386
```

</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 round = require( '@stdlib/math/base/special/round' );
var logpmf = require( '@stdlib/stats/base/dists/geometric/logpmf' );

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

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

</section>

<!-- /.examples -->

<section class="links">

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

[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function

</section>

<!-- /.links -->
