# @stdlib/stats-base-dists-normal-quantile

Normal distribution quantile function.

## Usage no npm install needed!

<script type="module">
import stdlibStatsBaseDistsNormalQuantile from 'https://cdn.skypack.dev/@stdlib/stats-base-dists-normal-quantile';
</script>

# Quantile Function

Normal distribution quantile function.

The quantile function for a normal random variable is

for 0 <= p <= 1, where µ is the mean and σ is the standard deviation.

## Installation

npm install @stdlib/stats-base-dists-normal-quantile


## Usage

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


#### quantile( p, mu, sigma )

Evaluates the quantile function for a normal distribution with parameters mu (mean) and sigma (standard deviation).

var y = quantile( 0.5, 0.0, 1.0 );
// returns 0.0

y = quantile( 0.2, 4.0, 2.0 );
// returns ~2.317


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

var y = quantile( 1.9, 0.0, 1.0 );
// returns NaN

y = quantile( -0.1, 0.0, 1.0 );
// returns NaN


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

var y = quantile( NaN, 0.0, 1.0 );
// returns NaN

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

y = quantile( 0.0, 0.0, NaN );
// returns NaN


If provided sigma < 0, the function returns NaN.

var y = quantile( 0.4, 0.0, -1.0 );
// returns NaN


If provided sigma = 0, the function evaluates the quantile function of a degenerate distribution centered at mu.

var y = quantile( 0.3, 8.0, 0.0 );
// returns 8.0

y = quantile( 0.9, 8.0, 0.0 );
// returns 8.0


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

Returns a function for evaluating the quantile function of a normal distribution with parameters mu and sigma.

var myquantile = quantile.factory( 10.0, 2.0 );

var y = myquantile( 0.2 );
// returns ~8.317

y = myquantile( 0.8 );
// returns ~11.683


## Examples

var randu = require( '@stdlib/random-base-randu' );
var quantile = require( '@stdlib/stats-base-dists-normal-quantile' );

var sigma;
var mu;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
p = randu();
mu = (randu() * 10.0) - 5.0;
sigma = randu() * 20.0;
y = quantile( p, mu, sigma );
console.log( 'p: %d, µ: %d, σ: %d, Q(p;µ,σ): %d', p, 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.