Pareto (Type I) distribution cumulative distribution function.
The cumulative distribution function for a Pareto (Type I) random variable is
and zero otherwise. In the equation, alpha > 0
is the shape parameter and beta > 0
is the scale parameter.
$ npm install distributions-pareto-type1-cdf
For use in the browser, use browserify.
var cdf = require( 'distributions-pareto-type1-cdf' );
Evaluates the cumulative distribution function for the Pareto (Type I) 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
x = [ -4, -2, 0, 2, 4 ];
out = cdf( x );
// returns [ 0, 0, 0, 0.5, 0.75 ]
x = new Float32Array( x );
out = cdf( x );
// returns Float64Array( [0,0,0,0.5,0.75] )
x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i - 3;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ -3 -2
-1 0
1 2 ]
*/
out = cdf( mat );
/*
[ 0 0
0 0
0 0.5 ]
*/
The function accepts the following options
:
- alpha: shape parameter. Default:
1
. - beta: scale 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 Pareto distribution is a function of two parameters: alpha > 0
(shape parameter) and beta > 0
(scale parameter). By default, alpha
is equal to 1
and beta
is equal to 1
. To adjust either parameter, set the corresponding option.
var x = [ -4, -2, 0, 2, 4 ];
var out = cdf( x, {
'alpha': 7,
'beta': 1.5
});
// returns [ 0, 0, 0, ~0.867, ~0.999 ]
For non-numeric arrays
, provide an accessor function
for accessing array
values.
var data = [
[0,-4],
[1,-2],
[2,0],
[3,2],
[4,4],
];
function getValue( d, i ) {
return d[ 1 ];
}
var out = cdf( data, {
'accessor': getValue
});
// returns [ 0, 0, 0, 0.5, 0.75 ]
To deepset an object array
, provide a key path and, optionally, a key path separator.
var data = [
{'x':[0,-4]},
{'x':[1,-2]},
{'x':[2,0]},
{'x':[3,2]},
{'x':[4,4]},
];
var out = cdf( data, {
'path': 'x/1',
'sep': '/'
});
/*
[
{'x':[0,0]},
{'x':[1,0]},
{'x':[2,0]},
{'x':[3,0.5]},
{'x':[4,0.75]},
]
*/
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 Float64Array( [-4,-2,0,2,4] );
out = cdf( x, {
'dtype': 'float32'
});
// returns Float32Array( [0,0,0,0.5,0.75] )
// Works for plain arrays, as well...
out = cdf( [-4,-2,0,2,4], {
'dtype': 'float32'
});
// returns Float32Array( [0,0,0,0.5,0.75] )
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 = [ -4, -2, 0, 2, 4 ];
out = cdf( x, {
'copy': false
});
// returns [ 0, 0, 0, 0.5, 0.75 ]
bool = ( x === out );
// returns true
x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i - 3 ;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ -3 -2
-1 0
1 2 ]
*/
out = cdf( mat, {
'copy': false
});
/*
[ 0 0
0 0
0 0.5 ]
*/
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-pareto-type1-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 - 5;
}
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 - 5;
}
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.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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