distributions-poisson-quantile

Quantile Function
===
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> Poisson distribution quantile function.

The quantile function for a Poisson random variable returns for 0 <= p <= 1 the smallest non-negative integer for which

where F is the cumulative distribution function (CDF) of a Poisson distribution with mean parameter lambda > 0.

Installation

`` bash
$ npm install distributions-poisson-quantile
`

For use in the browser, use browserify.

Usage

` javascript
var quantile = require( 'distributions-poisson-quantile' );
`

#### quantile( p[, options] )

Evaluates the quantile function for the Poisson distribution. p may be either a number between 0 and 1, an array, a typed array, or a matrix.

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

out = quantile( 0.25 );
// returns 0

x = [ 0, 0.2, 0.4, 0.6, 0.8, 1 ];
out = quantile( x );
// returns [ 0, 0, 1, 1, 2, +Infinity ]

x = new Float32Array( x );
out = quantile( x );
// returns Float64Array( [0,0,1,1,2,+Infinity] )

x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i / 6;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ 0 1/6
2/6 3/6
4/5 5/6 ]
*/

out = quantile( mat );
/*
[ 0 0
0 1
1 2 ]
*/
`

The function accepts the following options:

* __lambda__: mean parameter. 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 Poisson distribution is a function of one parameter: lambda > 0(mean parameter). By default, lambda is equal to 1. To adjust it, set the corresponding option.

` javascript
var x = [ 0, 0.2, 0.4, 0.6, 0.8, 1 ];

var out = quantile( x, {
'lambda': 6
});
// returns [ 0, 4, 5, 6, 8, +Infinity ]
`

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

` javascript
var data = [
[0,0],
[1,0.2],
[2,0.4],
[3,0.6],
[4,0.8],
[5,1]
];

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

var out = quantile( data, {
'accessor': getValue
});
// returns [ 0, 0, 1, 1, 2, +Infinity ]
`


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

` javascript
var data = [
{'x':[0,0]},
{'x':[1,0.2]},
{'x':[2,0.4]},
{'x':[3,0.6]},
{'x':[4,0.8]},
{'x':[5,1]}
];

var out = quantile( data, {
'path': 'x/1',
'sep': '/'
});
/*
[
{'x':[0,0]},
{'x':[1,0]},
{'x':[2,1]},
{'x':[3,1]},
{'x':[4,2]},
{'x':[5,+Infinity]}
]
*/

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 Float32Array( [0.2,0.4,0.6,0.8] );

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

// Works for plain arrays, as well...
out = quantile( [0.2,0.4,0.6,0.8], {
'dtype': 'uint8'
});
// returns Uint8Array( [0,1,1,2] )
`

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, 0.2, 0.4, 0.6, 0.8, 1 ];

out = quantile( x, {
'copy': false
});
// returns [ 0, 0, 1, 1, 2, +Infinity ]

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

x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i / 6 ;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ 0 1/6
2/6 3/6
4/5 5/6 ]
*/

out = quantile( mat, {
'copy': false
});
/*
[ 0 0
0 1
1 2 ]
*/

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

Notes

* For any p outside the interval [0,1], the the evaluated quantile function is NaN.

`javascript
var out;

out = quantile( 1.1 );
// returns NaN

out = quantile( -0.1 );
// returns NaN
`

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

` javascript
var data, out;

out = quantile( null );
// returns NaN

out = quantile( true );
// returns NaN

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

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

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

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

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

Examples

` javascript
var quantile = require( 'distributions-poisson-quantile' ),
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 ] = i / 10;
}
out = quantile( data );

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

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

// Typed arrays...
data = new Float32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = i / 10;
}
out = quantile( data );

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

// Matrices (custom output data type)...
out = quantile( 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.

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[npm-url]: https://npmjs.org/package/distributions-poisson-quantile

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

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[dependencies-url]: https://david-dm.org/distributions-io/poisson-quantile

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[dev-dependencies-url]: https://david-dm.org/dev/distributions-io/poisson-quantile

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