Raw-moments NPM

raw-moments

• Introduction • Limitations • Usage • Test • License •

Introduction

Returns the average(s) of values raised to one or more exponents: E(x,k) = ∑(x^k)/n

If a sample array and an exponent are provided, returns a single raw moment (origin moment)

f(A,b) = ∑(a^b) / n

If a sample array and an array of length N are provided, returns the same array filled moments 1 to N.

f(A, B) = ∑(a)/n, ∑(a^2)/n, ∑(a^3), ...

Limitations

While Kahan summation is used internally to reduce floating point errors, care must be taken if different sums are to be substracted for variance or skew calculations.

For large data sets that are far from the origin (ie 0 would fall outside the range of values) the significant order of magnitude between terms will cause significant errors during substractions.

Usage

single power

With a single exponent, rawMoments(samples, k) return the single k^th raw moment (aka origin moment).

var rawMoments = require('raw-moments')
rawMoments([0, 1, 2], 2)    // return (0 + 1^2 + 2^2)/3 = 5/3
rawMoments([1/4, 1/2, 1], -1)    // return (4 + 2 + 1)/3 = 5/3

multiple powers

The actual use case is to obtain multiple k^th order raw moments in a single pass. The maximum order is the length of the parameter array and the results will be inserted in this Array before it is returned.

var rawMoments = require('raw-moments')
rawMoments([0,1,2], Array(4))    // returns [1, 5/3, 3, 17/3]

Values in the second parameter array are replaced with the actual result and the same array is returned

var rawMoments = require('raw-moments')
var results = [0, 0, 99]    //initial values not important, only the array length
rawMoments([2,2], results)    // results = [4, 8, 16]

edge cases

var rawMoments = require('raw-moments')
rawMoments([], Array(3))    // returns [NaN, NaN, NaN]
rawMoments([0,1,2])    // returns the simple average (5/3)
rawMoments([0,1,2], [])    // returns the empty set []