# Logarithm of Cumulative Distribution Function

Evaluate the natural logarithm of the cumulative distribution function (CDF) for a normal distribution.

## Installation

`npm install @stdlib/stats-base-dists-normal-logcdf`

Alternatively,

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

## Usage

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

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

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

```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`.

```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`.

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

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

```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) of a normal distribution with parameters `mu` (mean) and `sigma` (standard deviation).

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

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

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

## Examples

```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 );
}```

## Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.