distributions-normal-pdf

Probability Density Function
===
[![NPM version][npm-image]][npm-url] [![Build Status][travis-image]][travis-url] [![Coverage Status][codecov-image]][codecov-url] [![Dependencies][dependencies-image]][dependencies-url]

> Normal distribution probability density function (PDF).

The probability density function (PDF) for a normal random variable is

where mu is the mean and sigma > 0 is the standard deviation.

Installation

`` bash
$ npm install distributions-normal-pdf
`

For use in the browser, use browserify.

Usage

` javascript
var pdf = require( 'distributions-normal-pdf' );
`

#### pdf( x[, options] )

Evaluates the probability density function (PDF) for the normal distribution. x may be either a number, an array, a typed array, or a matrix.

` javascript
var matrix = require( 'dstructs-matrix' ),
mat,
out,
x,
i;

// Standard Normal Distribution (mu=1, sigma=1):

out = pdf( 1 );
// returns 0.2419707

out = pdf( -1 );
// returns 0.2419707

x = [ 0, 0.5, 1, 1.5, 2, 2.5 ];
out = pdf( x );
// returns [ ~0.399, ~0.352, ~0.242, ~0.13, ~0.054, ~0.0175 ]

x = new Float32Array( x );
out = pdf( x );
// returns Float64Array( [~0.399,~0.352,~0.242,~0.13,~0.054,~0.0175] )

x = new Float64Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i*0.5;
}
mat = matrix( x, [3,2], 'float64' );
/*
[ 0 0.5
1 1.5
2 2.5 ]
*/

out = pdf( mat );
/*
[ ~0.399 ~0.352
~0.242 ~0.13
~0.054 ~0.0175 ]
*/
`

The function accepts the following options:

* __mu__: mean . Default: 0.
* __sigma__: standard deviation. Default: 1.
* __accessor__: accessor function for accessing array values.
* __dtype__: output typed array or matrix data type. Default: float64.
* __copy__: boolean indicating if the function should return a new data structure. Default: true.
* __path__: deepget/deepset key path.
* __sep__: deepget/deepset key path separator. Default: '.'.

A normal distribution is a function of two parameters: mu(mean) and sigma > 0(standard deviation). By default, mu is equal to 0 and sigma is equal to 1. To adjust either parameter, set the corresponding option.

` javascript
var x = [ 0, 0.5, 1, 1.5, 2, 2.5 ];

var out = pdf( x, {
'mu': 2,
'sigma': 2,
});
// returns [ ~0.121, ~0.151, ~0.176, ~0.193, ~0.199, ~0.193 ]
`

For non-numeric arrays, provide an accessor function for accessing array values.

` javascript
var data = [
[0,0],
[1,0.5],
[2,1],
[3,1.5],
[4,2],
[5,2.5]
];

function getValue( d, i ) {
return d[ 1 ];
}

var out = pdf( data, {
'accessor': getValue
});
// returns [ ~0.399, ~0.352, ~0.242, ~0.13, ~0.054, ~0.0175 ]
`


To deepset an object array, provide a key path and, optionally, a key path separator.

` javascript
var data = [
{'x':[0,0]},
{'x':[1,0.5]},
{'x':[2,1]},
{'x':[3,1.5]},
{'x':[4,2]},
{'x':[5,2.5]}
];

var out = pdf( data, {
'path': 'x/1',
'sep': '/'
});
/*
[
{'x':[0,~0.399]},
{'x':[1,~0.352]},
{'x':[2,~0.242]},
{'x':[3,~0.13]},
{'x':[4,~0.054]},
{'x':[5,~0.0175]}
]
*/
var bool = ( data === out );
// returns true
`

By default, when provided a typed array or matrix, the output data structure is float64 in order to preserve precision. To specify a different data type, set the dtype option (see matrix for a list of acceptable data types).

` javascript
var x, out;

x = new Int8Array( [0,1,2,3,4] );

out = pdf( x, {
'mu': 2,
'sigma': 2,
'dtype': 'int32'
});
// returns Int32Array( [0,0,1,0,0] )

// Works for plain arrays, as well...
out = pdf( [0,0.5,1,1.5,2], {
'mu': 2,
'sigma': 2,
'dtype': 'uint8'
});
// returns Uint8Array( [0,0,1,0,0] )
`

By default, the function returns a new data structure. To mutate the input data structure (e.g., when input values can be discarded or when optimizing memory usage), set the copy option to false.

` javascript
var bool,
mat,
out,
x,
i;

x = [ 0, 0.5, 1, 1.5, 2 ];

out = pdf( x, {
'copy': false
});
// returns [ ~0.399, ~0.352, ~0.242, ~0.13, ~0.054, ~0.0175 ]

bool = ( x === out );
// returns true

x = new Int16Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i*0.5;
}
mat = matrix( x, [3,2], 'int16' );
/*
[ 0 0.5
1 1.5
2 2.5 ]
*/

out = pdf( mat, {
'copy': false
});
/*
[ ~0.399 ~0.352
~0.242 ~0.13
~0.054 ~0.0175 ]
*/

bool = ( mat === out );
// returns true
`

Notes

* If an element is __not__ a numeric value, the evaluated PDF is NaN.

` javascript
var data, out;

out = pdf( null );
// returns NaN

out = pdf( true );
// returns NaN

out = pdf( {'a':'b'} );
// returns NaN

out = pdf( [ true, null, [] ] );
// returns [ NaN, NaN, NaN ]

function getValue( d, i ) {
return d.x;
}
data = [
{'x':true},
{'x':[]},
{'x':{}},
{'x':null}
];

out = pdf( data, {
'accessor': getValue
});
// returns [ NaN, NaN, NaN, NaN ]

out = pdf( data, {
'path': 'x'
});
/*
[
{'x':NaN},
{'x':NaN},
{'x':NaN,
{'x':NaN}
]
*/
`

* Be careful when providing a data structure which contains non-numeric elements and specifying an integer output data type, as NaN values are cast to 0.

` javascript
var out = pdf( [ true, null, [] ], {
'dtype': 'int8'
});
// returns Int8Array( [0,0,0] );
`

Examples

` javascript
var pdf = require( 'distributions-normal-pdf' ),
matrix = require( 'dstructs-matrix' );

var data,
mat,
out,
tmp,
i;

// Plain arrays...
data = new Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = -2.5 + i * 0.5;
}
out = pdf( data );

// Object arrays (accessors)...
function getValue( d ) {
return d.x;
}
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': data[ i ]
};
}
out = pdf( data, {
'accessor': getValue
});

// Deep set arrays...
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': [ i, data[ i ].x ]
};
}
out = pdf( data, {
'path': 'x/1',
'sep': '/'
});

// Typed arrays...
data = new Float32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = -2.5 + i * 0.5;
}
out = pdf( data );

// Matrices...
mat = matrix( data, [5,2], 'float32' );
out = pdf( mat );

// Matrices (custom output data type)...
out = pdf( mat, {
'dtype': 'uint8'
});
`

To run the example code from the top-level application directory,

` bash
$ node ./examples/index.js
`

Tests

$3

Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:

` bash
$ make test
`

All new feature development should have corresponding unit tests to validate correct functionality.

$3

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

` bash
$ make test-cov
`

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

` bash
$ make view-cov
``

---

License

MIT license.

Copyright

Copyright © 2015. The Compute.io Authors.

[npm-image]: http://img.shields.io/npm/v/distributions-normal-pdf.svg
[npm-url]: https://npmjs.org/package/distributions-normal-pdf

[travis-image]: http://img.shields.io/travis/distributions-io/normal-pdf/master.svg
[travis-url]: https://travis-ci.org/distributions-io/normal-pdf

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[codecov-url]: https://codecov.io/github/distributions-io/normal-pdf?branch=master

[dependencies-image]: http://img.shields.io/david/distributions-io/normal-pdf.svg
[dependencies-url]: https://david-dm.org/distributions-io/normal-pdf

[dev-dependencies-image]: http://img.shields.io/david/dev/distributions-io/normal-pdf.svg
[dev-dependencies-url]: https://david-dm.org/dev/distributions-io/normal-pdf

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[github-issues-url]: https://github.com/distributions-io/normal-pdf/issues