Rayleigh distribution quantile function.
The quantile function for a Rayleigh random variable is
for 0 <= p < 1
, where sigma
is the scale parameter.
$ npm install distributions-rayleigh-quantile
For use in the browser, use browserify.
var quantile = require( 'distributions-rayleigh-quantile' );
Evaluates the quantile function for the Rayleigh distribution. p
may be either a number
between 0
and 1
, an array
, a typed array
, or a matrix
.
var matrix = require( 'dstructs-matrix' ),
mat,
out,
x,
i;
out = quantile( 0.25 );
// returns ~0.759
x = [ 0, 0.2, 0.4, 0.6, 0.8, 1 ];
out = quantile( x );
// returns [ 0, ~0.668, ~1.011, ~1.354, ~1.794, +Infinity ]
x = new Float32Array( x );
out = quantile( x );
// returns Float64Array( [0,~0.668,~1.011,~1.354,~1.794,+Infinity] )
x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i / 6;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ 0 1/6
2/6 3/6
4/5 5/6 ]
*/
out = quantile( mat );
/*
[ 0 ~0.604
~0.901 ~1.18
~1.48 ~1.89 ]
*/
The function accepts the following options
:
- sigma: 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 Rayleigh distribution is a function of one parameter: sigma
(scale parameter). By default, sigma
is equal to 1
. To adjust it, set the corresponding option.
var x = [ 0, 0.2, 0.4, 0.6, 0.8, 1 ];
var out = quantile( x, {
'sigma': 3
});
// returns [ 0, ~2, ~3.03, ~4.06, ~5.38, +Infinity ]
For non-numeric arrays
, provide an accessor function
for accessing array
values.
var data = [
[0,0],
[1,0.2],
[2,0.4],
[3,0.6],
[4,0.8],
[5,1]
];
function getValue( d, i ) {
return d[ 1 ];
}
var out = quantile( data, {
'accessor': getValue
});
// returns [ 0, ~0.668, ~1.011, ~1.354, ~1.794, +Infinity ]
To deepset an object array
, provide a key path and, optionally, a key path separator.
var data = [
{'x':[0,0]},
{'x':[1,0.2]},
{'x':[2,0.4]},
{'x':[3,0.6]},
{'x':[4,0.8]},
{'x':[5,1]}
];
var out = quantile( data, {
'path': 'x/1',
'sep': '/'
});
/*
[
{'x':[0,0]},
{'x':[1,~0.668]},
{'x':[2,~1.011]},
{'x':[3,~1.354]},
{'x':[4,~1.794]},
{'x':[5,+Infinity]}
]
*/
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 Float32Array( [0.2,0.4,0.6,0.8] );
out = quantile( x, {
'dtype': 'int32'
});
// returns Int32Array( [0,1,1,1] )
// Works for plain arrays, as well...
out = quantile( [0.2,0.4,0.6,0.8], {
'dtype': 'uint8'
});
// returns Uint8Array( [0,1,1,1] )
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, 0.2, 0.4, 0.6, 0.8, 1 ];
out = quantile( x, {
'copy': false
});
// returns [ 0, ~0.668, ~1.011, ~1.354, ~1.794, +Infinity ]
bool = ( x === out );
// returns true
x = new Float32Array( 6 );
for ( i = 0; i < 6; i++ ) {
x[ i ] = i / 6 ;
}
mat = matrix( x, [3,2], 'float32' );
/*
[ 0 1/6
2/6 3/6
4/5 5/6 ]
*/
out = quantile( mat, {
'copy': false
});
/*
[ 0 ~0.604
~0.901 ~1.18
~1.48 ~1.89 ]
*/
bool = ( mat === out );
// returns true
-
For any
p
outside the interval[0,1]
, the the evaluated quantile function isNaN
.var out; out = quantile( 1.1 ); // returns NaN out = quantile( -0.1 ); // returns NaN
-
If an element is not a numeric value, the evaluated quantile function is
NaN
.var data, out; out = quantile( null ); // returns NaN out = quantile( true ); // returns NaN out = quantile( {'a':'b'} ); // returns NaN out = quantile( [ true, null, [] ] ); // returns [ NaN, NaN, NaN ] function getValue( d, i ) { return d.x; } data = [ {'x':true}, {'x':[]}, {'x':{}}, {'x':null} ]; out = quantile( data, { 'accessor': getValue }); // returns [ NaN, NaN, NaN, NaN ] out = quantile( 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 = quantile( [ true, null, [] ], { 'dtype': 'int8' }); // returns Int8Array( [0,0,0] );
var quantile = require( 'distributions-rayleigh-quantile' ),
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 / 10;
}
out = quantile( data );
// Object arrays (accessors)...
function getValue( d ) {
return d.x;
}
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': data[ i ]
};
}
out = quantile( data, {
'accessor': getValue
});
// Deep set arrays...
for ( i = 0; i < data.length; i++ ) {
data[ i ] = {
'x': [ i, data[ i ].x ]
};
}
out = quantile( data, {
'path': 'x/1',
'sep': '/'
});
// Typed arrays...
data = new Float32Array( 10 );
for ( i = 0; i < data.length; i++ ) {
data[ i ] = i / 10;
}
out = quantile( data );
// Matrices...
mat = matrix( data, [5,2], 'float32' );
out = quantile( mat );
// Matrices (custom output data type)...
out = quantile( 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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