Negative binomial distribution cumulative distribution function.
The cumulative distribution function for a negative binomial random variable is
where r is the number of failures until experiment is stopped, p is the success probability in each trial and I is the lower regularized incomplete beta function.
$ npm install distributions-negative-binomial-cdfFor use in the browser, use browserify.
var cdf = require( 'distributions-negative-binomial-cdf' );Evaluates the cumulative distribution function for the negative binomial 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 = cdf( 1 );
// returns 0.75
x = [ -1, 0, 1, 2, 3 ];
out = cdf( x );
// returns [ 0, 0.5, 0.75, 0.875, 0.9375 ]
x = new Float32Array( x );
out = cdf( x );
// returns Float64Array( [0,0.5,0.75,0.875,0.9375] )
x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ 0 1
2 3
4 5 ]
*/
out = cdf( mat );
/*
[ 0.5 0.75
0.875 ~0.938
~0.969 ~0.984 ]
*/The function accepts the following options:
- r: number of failures until experiment is stopped. Default:
1. - p: success probability. Default:
0.5. - accessor: accessor
functionfor accessingarrayvalues. - dtype: output
typed arrayormatrixdata type. Default:float64. - copy:
booleanindicating if thefunctionshould return a new data structure. Default:true. - path: deepget/deepset key path.
- sep: deepget/deepset key path separator. Default:
'.'.
A negative binomial distribution is a function of two parameters: r(number of failures until experiment is stopped) and 0 < p < 1(success probability). By default, r is equal to 1 and p is equal to 0.5. To adjust either parameter, set the corresponding option.
var x = [ -1, 0, 1, 2, 3 ];
var out = cdf( x, {
'r': 6,
'p': 0.4
});
// returns [ ~0.0041, ~0.0188, ~0.0498, ~0.0994, ~0.166, ~0.247 ]For non-numeric arrays, provide an accessor function for accessing array values.
var data = [
[0,-1],
[1,0],
[2,1],
[3,2],
[4,3],
];
function getValue( d, i ) {
return d[ 1 ];
}
var out = cdf( data, {
'accessor': getValue
});
// returns [ 0, 0.5, 0.75, 0.875, 0.9375 ]To deepset an object array, provide a key path and, optionally, a key path separator.
var data = [
{'x':[0,-1]},
{'x':[1,0]},
{'x':[2,1]},
{'x':[3,2]},
{'x':[4,3]},
];
var out = cdf( data, {
'path': 'x/1',
'sep': '/'
});
/*
[
{'x':[0,0]},
{'x':[1,0.5]},
{'x':[2,0.75]},
{'x':[3,0.875]},
{'x':[4,0.9375]},
]
*/
var bool = ( data === out );
// returns trueBy 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 Float64Array( [-1,0,1,2,3] );
out = cdf( x, {
'dtype': 'float32'
});
// returns Float32Array( [0,0.5,0.75,0.875,0.9375] )
// Works for plain arrays, as well...
out = cdf( [-4,-2,0,2,4], {
'dtype': 'float32'
});
// returns Float32Array( [0,0.5,0.75,0.875,0.9375] )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 = [ -1, 0, 1, 2, 3 ];
out = cdf( x, {
'copy': false
});
// returns [ 0, 0.5, 0.75, 0.875, 0.9375 ]
bool = ( x === out );
// returns true
x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ 0 1
2 3
4 5 ]
*/
out = cdf( mat, {
'copy': false
});
/*
[ 0.5 0.75
0.875 ~0.938
~0.969 ~0.984 ]
*/
bool = ( mat === out );
// returns true-
If an element is not a numeric value, the evaluated cumulative distribution function is
NaN.var data, out; out = cdf( null ); // returns NaN out = cdf( true ); // returns NaN out = cdf( {'a':'b'} ); // returns NaN out = cdf( [ true, null, [] ] ); // returns [ NaN, NaN, NaN ] function getValue( d, i ) { return d.x; } data = [ {'x':true}, {'x':[]}, {'x':{}}, {'x':null} ]; out = cdf( data, { 'accessor': getValue }); // returns [ NaN, NaN, NaN, NaN ] out = cdf( data, { 'path': 'x' }); /* [ {'x':NaN}, {'x':NaN}, {'x':NaN, {'x':NaN} ] */
var cdf = require( 'distributions-negative-binomial-cdf' ),
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;
}
out = cdf( data );
// Object arrays (accessors)...
function getValue( d ) {
return d.x;
}
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': data[ i ]
};
}
out = cdf( data, {
'accessor': getValue
});
// Deep set arrays...
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': [ i, data[ i ].x ]
};
}
out = cdf( data, {
'path': 'x/1',
'sep': '/'
});
// Typed arrays...
data = new Float32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = i;
}
out = cdf( data );
// Matrices...
mat = matrix( data, [5,2], 'float32' );
out = cdf( mat );
// Matrices (custom output data type)...
out = cdf( mat, {
'dtype': 'uint8'
});To run the example code from the top-level application directory,
$ node ./examples/index.jsUnit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:
$ make testAll 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-covIstanbul creates a ./reports/coverage directory. To access an HTML version of the report,
$ make view-covCopyright © 2015. The Compute.io Authors.
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