Normal

Normal distribution.

Usage

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

normal

Normal distribution.

var dist = normal;
// returns {...}

The namespace contains the following distribution functions:

cdf( x, mu, sigma ): normal distribution cumulative distribution function.
logcdf( x, mu, sigma ): evaluate the natural logarithm of the cumulative distribution function (CDF) for a normal distribution.
logpdf( x, mu, sigma ): evaluate the natural logarithm of the probability density function (PDF) for a normal distribution.
mgf( t, mu, sigma ): normal distribution moment-generating function (MGF).
pdf( x, mu, sigma ): normal distribution probability density function (PDF).
quantile( p, mu, sigma ): normal distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

entropy( mu, sigma ): normal distribution differential entropy.
kurtosis( mu, sigma ): normal distribution excess kurtosis.
mean( mu, sigma ): normal distribution expected value.
median( mu, sigma ): normal distribution median.
mode( mu, sigma ): normal distribution mode.
skewness( mu, sigma ): normal distribution skewness.
stdev( mu, sigma ): normal distribution standard deviation.
variance( mu, sigma ): normal distribution variance.

The namespace contains a constructor function for creating a normal distribution object.

Normal( [mu, sigma] ): normal distribution constructor.

var Normal = require( '@stdlib/stats/base/dists/normal' ).Normal;

var dist = new Normal( 2.0, 4.0 );

var y = dist.pdf( 2.0 );
// returns ~0.1

Examples

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

/*
A bakery is analyzing cake baking times to ensure consistency and better schedule their baking processes.

The Central Limit Theorem (CLT) states that the average baking times from many batches will follow a normal distribution if there are enough batches (typically n > 30).

Assuming each record represents the average baking time per batch and the bakery has collected the following data:

-      Mean baking time (μ/mu): 20 minutes.
-      Standard deviation in baking time (σ/sigma): 3 minutes.

We can model the average bake times using a normal distribution with μ (mu) = 20.0 minutes and σ = 3.0 minutes.
*/

var mu = 20.0;
var sigma = 3.0;

var normalDist = new normal.Normal( mu, sigma );

// Output the standard deviation of the baking times:
console.log( normalDist.sigma );
// => 3.0

// Adjust distribution parameters
normalDist.sigma = 4.0;

// Adjusted standard deviation to reflect different variance scenario:
console.log( normalDist.sigma );
// => 4.0

// Excess kurtosis of a normal distribution (measure of "tailedness"):
console.log( normalDist.kurtosis );
// => 0.0

// Median baking time:
console.log( normalDist.median );
// => 20.0

// Variance of the baking times after adjusting sigma:
console.log( normalDist.variance );
// => 16.0

// Probability density function at the mean baking time:
console.log( normal.pdf( 20.0, mu, sigma ) );
// => ~0.133

// Cumulative distribution function at the mean (portion of times ≤ 20 minutes):
console.log( normal.cdf( 20.0, mu, sigma ) );
// => ~0.5

// 50th percentile (median) of the baking times:
console.log( normal.quantile( 0.5, mu, sigma ) );
// => 20.0

// Moment-generating function value at 0.5 (used in probability theory):
console.log( normal.mgf( 0.5, mu, sigma ) );
// => ~67846.291

// Entropy of the normal distribution (measure of uncertainty):
console.log( normal.entropy( mu, sigma ) );
// => ~2.518

// Mean baking time:
console.log( normal.mean( mu, sigma ) );
// => 20.0

// Median baking time:
console.log( normal.median( mu, sigma ) );
// => 20.0

// Mode of the baking times (most frequent value):
console.log( normal.mode( mu, sigma ) );
// => 20.0

// Variance of the baking times:
console.log( normal.variance( mu, sigma ) );
// => 9.0

// Skewness of the distribution (symmetry measure):
console.log( normal.skewness( mu, sigma ) );
// => 0.0

var myquantile = normal.quantile.factory( 20.0, 3.0 );

// 20th percentile (value below which 20% baking times fall):
console.log( myquantile( 0.2 ) );
// => ~17.475

// 80th percentile (value below which 80% baking times fall):
console.log( myquantile( 0.8 ) );
// => ~22.525

var mylogpdf = normal.logpdf.factory( 20.0, 3.0 );

// Logarithm of the probability density function at the mean:
console.log( mylogpdf( 20.0 ) );
// => ~-2.018

// Logarithm of the probability density function at 15 minutes:
console.log( mylogpdf( 15.0 ) );
// => ~-3.406