cumulative-distribution-function

Calculates statistical cumulative distribution function from data array of x values.

Installation

npm i cumulative-distribution-function -S

Dependencies

None. Suitable for usage on nodejs or on the browser, via browserify.

Initialization

const cdf = require('cumulative-distribution-function');

Usage

Pass a number data array as input. Do not pass strings that look like numbers. Invalid data may throw a TypeError

f = cdf(data) returns a function f, the empirical cumulative distribution function, a step function f(x) that counts the proportion of data less than or equal to the number input x.

The function returned by cdf(data) takes a number x and returns the proportion of values less than or equal to x.

New for v2.0: Passing string data (e.g."42") or other invalid, missing or empty data instead of numbers will throw a TypeError.

Pass clean data. Convert and clean up your data with something like:

const clean_data = raw_data
                    .map((v)=>(+v))
                    .filter((v)=>(isFinite(v)));

where the map function will convert stringified numbers (e.g. '123') to numbers; and the filter function will remove NaN's, +Infinity, and -Infinity.

The simple map/filter conversion above won't work for everybody.
For instance, +v converts '' or null to 0 which is kept, and undefined to NaN which is filtered out.

New for v2.1: Bisection loop limit

Error("cdf function exceeded 40 bisection iterations, aborting bisection loop")

The returned function f from f = cdf(data) will throw the above error instead of loop endlessly on invalid data. This helps in case an "attacker" (or simply poor code) changes the xs data array accessible at f.xs() to be string data or other invalid data. The limit of 40 bisections implies a data array size limit of roughly 2^40 or 10^12 entries. This limit is beyond 2021 browser and nodejs capabilities but is short enough to "fail quickly" in the case of an unusual failure in the bisection exit conditions.

Example

var mydata = [13,2,5,3,23,7,11,13,19,23];
var mycdf  = cdf(mydata); // cdf(mydata) returns a **function**, so mycdf is a **function**
mycdf(-5)  // 0.0 because all mydata are greater than -5
mycdf(2)  // 0.1 because 1 of 10 mydata are less than or equal to 2
mycdf(3)  // 0.2 because 2 of 10 mydata are less than or equal to 3
mycdf(13) // 0.7 because 7 of 10 mydata are less than or equal to 13
mycdf(19) // 0.8 because 8 of 10 mydata are less than or equal to 19
mycdf(20) // 0.8 because 8 of 10 mydata are less than or equal to 20
mycdf(25) // 1.0 because all mydata are less than or equal to 25
mycdf.xs() // returns [2,    3,  5,  7, 11, 13, 19, 23] from sorted, unique mydata
mycdf.ps() // returns [0.1,0.2,0.3,0.4,0.5,0.7,0.8,1.0] from corresponding cumulative proportions

Missing or Empty Data

Will throw TypeError

Tests

Use mocha framework.

Copyright

Copyright 2016- Paul Brewer, Economic and Financial Technology Consulting LLC

License

MIT