distributions-poisson-pmf
v0.0.2
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Poisson distribution probability mass function (PMF)
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Probability Mass Function
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
$ npm install distributions-poisson-pmf
For use in the browser, use browserify.
Usage
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
.
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 accessingarray
values. - dtype: output
typed array
ormatrix
data type. Default:float64
. - copy:
boolean
indicating if thefunction
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.
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.
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.
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).
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
.
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
.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, asNaN
values are cast to0
.var out = pmf( [ true, null, [] ], { 'dtype': 'int8' }); // returns Int8Array( [0,0,0] );
Examples
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,
$ node ./examples/index.js
Tests
Unit
Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:
$ make test
All new feature development should have corresponding unit tests to validate correct functionality.
Test Coverage
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:
$ make test-cov
Istanbul creates a ./reports/coverage
directory. To access an HTML version of the report,
$ make view-cov
License
Copyright
Copyright © 2015. The Compute.io Authors.