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

Standard library statistical functions.

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# Logarithm of Cumulative Distribution Function

> Evaluate the natural logarithm of the cumulative distribution function (CDF) for a [normal][normal-distribution] distribution.

<section class="intro">

</section>

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<section class="usage">

## Usage

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

#### logcdf( x, mu, sigma )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [normal][normal-distribution] distribution with parameters `mu` (mean) and `sigma` (standard deviation).

```javascript
var y = logcdf( 2.0, 0.0, 1.0 );
// returns ~-0.023

y = logcdf( -1.0, 4.0, 2.0 );
// returns ~-5.082
```

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 `sigma < 0`, the function returns `NaN`.

```javascript
var y = logcdf( 2.0, 0.0, -1.0 );
// returns NaN
```

If provided `sigma = 0`, the function evaluates the natural logarithm of the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at `mu`.

```javascript
var y = logcdf( 2.0, 8.0, 0.0 );
// returns -Infinity

y = logcdf( 8.0, 8.0, 0.0 );
// returns 0.0

y = logcdf( 10.0, 8.0, 0.0 );
// returns 0.0
```

#### logcdf.factory( mu, sigma )

Returns a `function` for evaluating the [cumulative distribution function][cdf] (CDF) of a [normal][normal-distribution] distribution with parameters `mu` (mean) and `sigma` (standard deviation).

```javascript
var mylogcdf = logcdf.factory( 10.0, 2.0 );

var y = mylogcdf( 10.0 );
// returns ~-0.693

y = mylogcdf( 5.0 );
// returns ~-5.082
```

</section>

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<section class="examples">

## Examples

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

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

var sigma;
var mu;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    mu = (randu() * 10.0) - 5.0;
    sigma = randu() * 20.0;
    y = logcdf( x, mu, sigma );
    console.log( 'x: %d, µ: %d, σ: %d, ln(F(x;µ,σ)): %d', x, mu, sigma, y );
}
```

</section>

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<section class="related">

</section>

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<section class="links">

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

[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution

[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution

</section>

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