Excess Kurtosis
Rayleigh distribution excess kurtosis.
The excess kurtosis for a Rayleigh random variable is
where sigma > 0
is the scale parameter.
Installation
$ npm install distributions-rayleigh-ekurtosis
For use in the browser, use browserify.
Usage
var ekurtosis = ;
ekurtosis( sigma[, opts] )
Computes the excess kurtosis for a Rayleigh distribution with parameter sigma
. sigma
may be either a number
, an array
, a typed array
, or a matrix
.
var matrix =datamatouti;out = ;// returns ~0.245sigma = 05 1 2 4 ;out = ;// returns [ ~0.245, ~0.245, ~0.245, ~0.245 ]sigma = sigma ;out = ;// returns Float64Array( [~0.245,~0.245,~0.245,~0.245] )sigma = ;/*[ 0.5 12 4 ]*/out = ;/*[ ~0.245 ~0.245~0.245 ~0.245 ]*/
The function accepts the following options
:
- 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:
'.'
.
For non-numeric arrays
, provide an accessor function
for accessing array
values.
var sigma =005112234;{return d 1 ;}var out =;// returns [ ~0.245, ~0.245, ~0.245, ~0.245 ]
To deepset an object array
, provide a key path and, optionally, a key path separator.
var sigma ='x':905'x':91'x':92'x':94;var out =;/*[{'x':[9,~0.245]},{'x':[9,~0.245]},{'x':[9,~0.245]},{'x':[9,~0.245]},]*/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 sigma out;sigma = 05124 ;out =;// returns Int32Array( [ 0,0,0,0 ] )// Works for plain arrays, as well...out =;// returns Int32Array( [ 0,0,0,0 ] )
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 sigmaboolmatouti;sigma = 05 1 2 4 ;out =;// returns [ ~0.245, ~0.245, ~0.245, ~0.245 ]bool = data === out ;// returns truemat = ;/*[ 0.5 12 4 ]*/out =;/*[ ~0.245 ~0.245~0.245 ~0.245 ]*/bool = mat === out ;// returns true
Notes
-
If an element is not a positive number, the excess kurtosis is
NaN
.var sigma out;out = ;// returns NaNout = ;// returns NaNout = ;// returns NaNout = ;// returns NaNout = ;// returns NaNout = ;// returns [ NaN, NaN, NaN ]{return dx;}sigma ='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 matrix =ekurtosis = ;var sigmamatouttmpi;// Plain arrays...sigma = 10 ;for i = 0; i < sigmalength; i++sigma i = i + 1;out = ;// Object arrays (accessors)...{return dx;}for i = 0; i < sigmalength; i++sigma i ='x': sigma i;out =;// Deep set arrays...for i = 0; i < sigmalength; i++sigma i ='x': i sigma i x;out =;// Typed arrays...sigma = 10 ;for i = 0; i < sigmalength; i++sigma i = i + 1;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.