raw-moments
v1.0.0
Published
single sample raw moment or array of multiple moments
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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 []
Test
In node, from the root folder type npm test
.
(test dependency is not included with the package and must be obtained from the git repository or npm)
License
Released under the MIT License
Test
In node, from the root folder type npm test
.
(test is not included with the package and must be obtained from the git repository)
License
Released under the MIT License