Compute an exponentially weighted standard deviation incrementally.

An exponentially weighted variance can be defined recursively as

upper S Subscript n Baseline equals StartLayout Enlarged left-brace 1st Row 1st Column 0 2nd Column if n equals 0 2nd Row 1st Column left-parenthesis 1 minus alpha right-parenthesis left-parenthesis upper S Subscript n minus 1 Baseline plus alpha left-parenthesis x Subscript n Baseline minus mu Subscript n minus 1 Baseline right-parenthesis squared right-parenthesis 2nd Column if n greater-than 0 EndLayout

where μ is the exponentially weighted mean. The exponentially weighted standard deviation is the square root of the exponentially weighted variance.


var increwstdev = require( '@stdlib/stats/incr/ewstdev' );

increwstdev( alpha )

Returns an accumulator function which incrementally computes an exponentially weighted standard deviation, where alpha is a smoothing factor between 0 and 1.

var accumulator = increwstdev( 0.5 );

accumulator( [x] )

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

var accumulator = increwstdev( 0.5 );

var s = accumulator();
// returns null

s = accumulator( 2.0 );
// returns 0.0

s = accumulator( 1.0 );
// returns 0.5

s = accumulator( 3.0 );
// returns ~0.83

s = accumulator();
// returns ~0.83


  • 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 all 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.


var randu = require( '@stdlib/random/base/randu' );
var increwstdev = require( '@stdlib/stats/incr/ewstdev' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = increwstdev( 0.5 );

// For each simulated datum, update the exponentially weighted standard deviation...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
console.log( accumulator() );
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