Probability Density Function
Cauchy distribution probability density function (PDF).
The probability density function (PDF) for a Cauchy random variable is
where gamma > 0
is the scale parameter and x0
is the location parameter.
Installation
$ npm install distributions-cauchy-pdf
For use in the browser, use browserify.
Usage
var pdf = ;
pdf( x[, options] )
Evaluates the probability density function (PDF) for the Cauchy distribution. x
may be either a number
, an array
, a typed array
, or a matrix
.
var matrix =matoutxi;out = ;// returns ~0.159out = ;// returns ~0.159x = 0 05 1 15 2 25 ;out = ;// returns [ ~0.318, ~0.255, ~0.159, ~0.0979, ~0.0637, ~0.0439 ]x = x ;out = ;// returns Float64Array( [~0.318,~0.255,~0.159,~0.0979,~0.0637,~0.0439] )x = 6 ;for i = 0; i < 6; i++x i = i * 05;mat = ;/*[ 0 0.51 1.52 2.5 ]*/out = ;/*[ ~0.318 ~0.255~0.159 ~0.0979~0.0637 ~0.0439 ]*/
The function accepts the following options
:
- gamma: scale parameter. Default:
1
. - x0: location parameter. Default:
0
. - 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 Cauchy distribution is a function of two parameters: gamma > 0
(scale parameter) and x0
(location parameter). By default, gamma
is equal to 1
and x0
is equal to 0
. To adjust either parameter, set the corresponding option.
var x = 0 05 1 15 2 25 ;var out =;// returns [ ~0.0315, ~0.122, ~3.18, ~0.122, ~0.0315, ~0.0141 ]
For non-numeric arrays
, provide an accessor function
for accessing array
values.
var data =001052131542525;{return d 1 ;}var out =;// returns [ ~0.318, ~0.255, ~0.159, ~0.0979, ~0.0637, ~0.0439 ]
To deepset an object array
, provide a key path and, optionally, a key path separator.
var data ='x':00'x':105'x':21'x':315'x':42'x':525;var out =;/*[{'x':[0,~0.318]},{'x':[1,~0.255]},{'x':[2,~0.159]},{'x':[3,~0.0979]},{'x':[4,0.0637]},{'x':[5,~0.0439]}]*/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 = 01234 ;out =;// returns Int32Array( [0,0,3,0,0] )// Works for plain arrays, as well...out =;// returns Uint8Array( [0,0,3,0,0] )
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 boolmatoutxi;x = 0 05 1 15 2 ;out =;// returns [ ~0.318, ~0.255, ~0.159, ~0.0979, ~0.0637, ~0.0439 ]bool = x === out ;// returns truex = 6 ;for i = 0; i < 6; i++x i = i * 05;mat = ;/*[ 0 0.51 1.52 2.5 ]*/out =;/*[ ~0.318 ~0.255~0.159 ~0.0979~0.0637 ~0.0439 ]*/bool = mat === out ;// returns true
Notes
-
If an element is not a numeric value, the evaluated PDF is
NaN
.var data out;out = ;// returns NaNout = ;// returns NaNout = ;// returns NaNout = ;// returns [ NaN, NaN, NaN ]{return dx;}data ='x':true'x':'x':{}'x':null;out =;// returns [ NaN, NaN, NaN, NaN ]out =;/*[{'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 =;// returns Int8Array( [0,0,0] );
Examples
var pdf =matrix = ;var datamatouttmpi;// Plain arrays...data = 10 ;for i = 0; i < datalength; i++data i = i * 05;out = ;// Object arrays (accessors)...{return dx;}for i = 0; i < datalength; i++data i ='x': data i;out =;// Deep set arrays...for i = 0; i < datalength; i++data i ='x': i data i x;out =;// Typed arrays...data = 10 ;for i = 0; i < datalength; i++data i = i * 05;out = ;// Matrices...mat = ;out = ;// Matrices (custom output data type)...out =;
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.