distributions-poisson-pmf

Probability Mass Function
===
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> Poisson distribution probability mass function (PMF).

The probability mass function (PMF) for a Poisson random variable is

where lambda > 0 is the mean parameter.

Installation

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

For use in the browser, use browserify.

Usage

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

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

Evaluates the probability mass function (PMF) for the Poisson 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;

out = pmf( 1 );
// returns ~0.368

out = pmf( -1 );
// returns 0

out = pmf( 0.5 );
// returns 0

x = [ 0, 1, 2, 3, 4, 5 ];
out = pmf( x );
// returns [ ~0.368, ~0.368, ~0.184, ~0.0613, ~0.0153, ~0.00307 ]

x = new Int8Array( x );
out = pmf( x );
// returns Float64Array( [~0.368,~0.368,~0.184,~0.0613,~0.0153,~0.00307] )

x = new Int16Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i;
}
mat = matrix( x, [3,2], 'int16' );
/*
[ 0 1
2 3
4 5 ]
*/

out = pmf( mat );
/*
[ ~0.368 ~0.368
~0.184 ~0.0613
~0.0153 ~0.00307 ]
*/
`

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, 1, 2, 3, 4, 5 ];

var out = pmf( x, {
'lambda': 5,
});
// returns [ ~0.00674, ~0.0337, ~0.0842, ~0.14, ~0.175, ~0.175 ]
`

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

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

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

var out = pmf( data, {
'accessor': getValue
});
// returns [ ~0.368, ~0.368, ~0.184, ~0.0613, ~0.0153, ~0.00307 ]
`


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

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

var out = pmf( data, {
'path': 'x/1',
'sep': '/'
});
/*
[
{'x':[0,~0.368]},
{'x':[1,~0.368]},
{'x':[2,~0.184]},
{'x':[3,~0.0613]},
{'x':[4,~0.0153]},
{'x':[5,~0.00307]}
]
*/

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 = pmf( x, {
'dtype': 'float32'
});
// returns Float32Array( [~0.00674,~0.0337,~0.0842,~0.14,~0.175] )

// Works for plain arrays, as well...
out = pmf( [0,1,2,3,4], {
'dtype': 'float32'
});
// returns Float32Array( [~0.00674,~0.0337,~0.0842,~0.14,~0.175] )
`

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, 1, 2, 3, 4, 5 ];

out = pmf( x, {
'copy': false
});
// returns [ ~0.368, ~0.368, ~0.184, ~0.0613, ~0.0153, ~0.00307 ]

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

x = new Int16Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i;
}
mat = matrix( x, [3,2], 'int16' );
/*
[ 0 1
2 3
4 5 ]
*/

out = pmf( mat, {
'copy': false
});
/*
[ ~0.368 ~0.368
~0.184 ~0.0613
~0.0153 ~0.00307 ]
*/

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

Notes

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

` javascript
var data, out;

out = pmf( null );
// returns NaN

out = pmf( true );
// returns NaN

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

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

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

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

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

Examples

` javascript
var pmf = require( 'distributions-poisson-pmf' ),
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 * 0.5;
}
out = pmf( data );

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

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

// Typed arrays...
data = new Int32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = i;
}
out = pmf( data );

// Matrices...
mat = matrix( data, [5,2], 'int32' );
out = pmf( mat );

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