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Compute a moving coefficient of variation (CV) incrementally.

For a window of size W, the corrected sample standard deviation is defined as

Equation for the corrected sample standard deviation.

and the arithmetic mean is defined as

The coefficient of variation (also known as relative standard deviation, RSD) is defined as


npm install @stdlib/stats-incr-mcv


var incrmcv = require( '@stdlib/stats-incr-mcv' );

incrmcv( window[, mean] )

Returns an accumulator function which incrementally computes a moving coefficient of variation. The window parameter defines the number of values over which to compute the moving coefficient of variation.

var accumulator = incrmcv( 3 );

If the mean is already known, provide a mean argument.

var accumulator = incrmcv( 3, 5.0 );

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated accumulated value. If not provided an input value x, the accumulator function returns the current accumulated value.

var accumulator = incrmcv( 3 );

var cv = accumulator();
// returns null

// Fill the window...
cv = accumulator( 2.0 ); // [2.0]
// returns 0.0

cv = accumulator( 1.0 ); // [2.0, 1.0]
// returns ~0.47

cv = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns 0.5

// Window begins sliding...
cv = accumulator( 7.0 ); // [1.0, 3.0, 7.0]
// returns ~0.83

cv = accumulator( 5.0 ); // [3.0, 7.0, 5.0]
// returns ~0.40

cv = accumulator();
// returns ~0.40


  • Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for at least W-1 future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
  • As W values are needed to fill the window buffer, the first W-1 returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
  • The coefficient of variation is typically computed on nonnegative values. The measure may lack meaning for data which can assume both positive and negative values.
  • For small and moderately sized samples, the accumulated value tends to be too low and is thus a biased estimator. Provided the generating distribution is known (e.g., a normal distribution), you may want to adjust the accumulated value or use an alternative implementation providing an unbiased estimator.


var randu = require( '@stdlib/random-base-randu' );
var incrmcv = require( '@stdlib/stats-incr-mcv' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrmcv( 5 );

// For each simulated datum, update the moving coefficient of variation...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
console.log( accumulator() );

See Also


This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.






Copyright © 2016-2024. The Stdlib Authors.

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