Compute a moving coefficient of variation (CV) incrementally.

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

s equals StartRoot StartFraction 1 Over upper W minus 1 EndFraction sigma-summation Underscript i equals 0 Overscript upper W minus 1 Endscripts left-parenthesis x Subscript i Baseline minus x overbar right-parenthesis squared EndRoot

and the arithmetic mean is defined as

x overbar equals StartFraction 1 Over upper W EndFraction sigma-summation Underscript i equals 0 Overscript upper W minus 1 Endscripts x Subscript i

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

c Subscript v Baseline equals StartFraction s Over x overbar EndFraction


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() );
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