Binomial distribution moment-generating function (MGF).
The moment-generating function for a Binomial random variable is
where the non-negative integer n
is the number of trials and 0 <= p <= 1
is the success probability.
$ npm install distributions-binomial-mgf
For use in the browser, use browserify.
var mgf = require( 'distributions-binomial-mgf' );
Evaluates the moment-generating function (MGF) for the Binomial distribution. t
may be either a number
, an array
, a typed array
, or a matrix
.
var matrix = require( 'dstructs-matrix' ),
mat,
out,
t,
i;
out = mgf( 1 );
// returns ~1.859
out = mgf( -1 );
// returns ~0.684
t = [ 0, 0.5, 1, 1.5, 2, 2.5 ];
out = mgf( t );
// returns [ 1, ~1.324, ~1.859, ~2.741, ~4.195, ~6.591 ]
t = new Int8Array( t );
out = mgf( t );
// returns Float64Array( [1,1,~1.859,~1.859,~4.195,~4.195] )
t = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
t[ i ] = i * 0.5;
}
mat = matrix( t, [3,2], 'float32' );
/*
[ 0 0.5
1 1.5
2 2.5 ]
*/
out = mgf( mat );
/*
[ 1.000 ~1.324
~1.859 ~2.741
~4.195, ~6.591 ]
*/
The function accepts the following options
:
- n: number of trials. Default:
1
. - p: success probability. Default:
0.5
. - 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 Binomial distribution is a function of two parameters: n
(number of trials) and p
(success probability). By default, n
is equal to 1
and p
is equal to 0.5
. To adjust either parameter, set the corresponding option.
var t = [ 0, 0.5, 1, 1.5, 2, 2.5 ];
var out = mgf( t, {
'n': 2,
'p': 0.6
});
// returns [ 1, ~2.681, ~8.377, ~29.475, ~112.919, ~458.224 ]
For non-numeric arrays
, provide an accessor function
for accessing array
values.
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 = mgf( data, {
'accessor': getValue
});
// returns [ 1, ~1.324, ~1.859, ~2.741, ~4.195, ~6.591 ]
To deepset an object array
, provide a key path and, optionally, a key path separator.
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 = mgf( data, {
'path': 'x/1',
'sep': '/'
});
/*
[
{'x':[0,1]},
{'x':[1,~1.324]},
{'x':[2,~1.859]},
{'x':[3,~2.741]},
{'x':[4,~4.195]},
{'x':[5,~6.591]}
]
*/
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 t, out;
t = new Int8Array( [0,1,2,3,4] );
out = mgf( t, {
'dtype': 'int32'
});
// returns Int32Array( [1,1,4,10,27] )
// Works for plain arrays, as well...
out = mgf( [0,1,2,3,4], {
'dtype': 'uint8'
});
// returns Uint8Array( [1,1,4,10,27] )
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,
t,
i;
t = [ 0, 0.5, 1, 1.5, 2, 2.5 ];
out = mgf( t, {
'copy': false
});
// returns [ 1, ~1.324, ~1.859, ~2.741, ~4.195, ~6.591 ]
bool = ( t === out );
// returns true
t = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
t[ i ] = i * 0.5;
}
mat = matrix( t, [3,2], 'float32' );
/*
[ 0 0.5
1 1.5
2 2.5 ]
*/
out = mgf( mat, {
'copy': false
});
/*
[ 1.000 ~1.324
~1.859 ~2.741
~4.195, ~6.591 ]
*/
bool = ( mat === out );
// returns true
-
If an element is not a numeric value, the evaluated MGF is
NaN
.var data, out; out = mgf( null ); // returns NaN out = mgf( true ); // returns NaN out = mgf( {'a':'b'} ); // returns NaN out = mgf( [ true, null, [] ] ); // returns [ NaN, NaN, NaN ] function getValue( d, i ) { return d.x; } data = [ {'x':true}, {'x':[]}, {'x':{}}, {'x':null} ]; out = mgf( data, { 'accessor': getValue }); // returns [ NaN, NaN, NaN, NaN ] out = mgf( 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 = mgf( [ true, null, [] ], { 'dtype': 'int8' }); // returns Int8Array( [0,0,0] );
var mgf = require( 'distributions-binomial-mgf' ),
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 = mgf( data );
// Object arrays (accessors)...
function getValue( d ) {
return d.x;
}
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': data[ i ]
};
}
out = mgf( data, {
'accessor': getValue
});
// Deep set arrays...
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': [ i, data[ i ].x ]
};
}
out = mgf( data, {
'path': 'x/1',
'sep': '/'
});
// Typed arrays...
data = new Float32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = i * 0.5;
}
out = mgf( data );
// Matrices...
mat = matrix( data, [5,2], 'float32' );
out = mgf( mat );
// Matrices (custom output data type)...
out = mgf( mat, {
'dtype': 'uint8'
});
To run the example code from the top-level application directory,
$ node ./examples/index.js
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.
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
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