Cumulative Distribution Function
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.
Installation
$ npm install distributions-pareto-type1-cdf
For use in the browser, use browserify.
Usage
var cdf = ;
cdf( x[, options] )
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 =matoutxi;out = ;// returns 0x = -4 -2 0 2 4 ;out = ;// returns [ 0, 0, 0, 0.5, 0.75 ]x = x ;out = ;// returns Float64Array( [0,0,0,0.5,0.75] )x = 6 ;for i = 0; i < 6; i++x i = i - 3;mat = ;/*[ -3 -2-1 01 2 ]*/out = ;/*[ 0 00 00 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 =;// returns [ 0, 0, 0, ~0.867, ~0.999 ]
For non-numeric arrays
, provide an accessor function
for accessing array
values.
var data =0-41-2203244;{return d 1 ;}var out =;// 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':20'x':32'x':44;var out =;/*[{'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 = -4-2024 ;out =;// returns Float32Array( [0,0,0,0.5,0.75] )// Works for plain arrays, as well...out =;// 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 boolmatoutxi;x = -4 -2 0 2 4 ;out =;// returns [ 0, 0, 0, 0.5, 0.75 ]bool = x === out ;// returns truex = 6 ;for i = 0; i < 6; i++x i = i - 3 ;mat = ;/*[ -3 -2-1 01 2 ]*/out =;/*[ 0 00 00 0.5 ]*/bool = mat === out ;// returns true
Notes
-
If an element is not a numeric value, the evaluated cumulative distribution function 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}]*/
Examples
var cdf =matrix = ;var datamatouttmpi;// Plain arrays...data = 10 ;for i = 0; i < datalength; i++data i = i - 5;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 - 5;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.