increwvariance

Compute an exponentially weighted variance incrementally.

An exponentially weighted variance can be defined recursively as

$$S_n = \begin{cases} 0 & \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) & \textrm{if}\ n > 0 \end{cases}$$

where μ is the exponentially weighted mean.

Usage

var increwvariance = require( '@stdlib/stats/incr/ewvariance' );

increwvariance( alpha )

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

var accumulator = increwvariance( 0.5 );

accumulator( [x] )

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

var accumulator = increwvariance( 0.5 );

var v = accumulator();
// returns null

v = accumulator( 2.0 );
// returns 0.0

v = accumulator( 1.0 );
// returns 0.25

v = accumulator( 3.0 );
// returns 0.6875

v = accumulator();
// returns 0.6875

Notes

• 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.

Examples

var randu = require( '@stdlib/random/base/randu' );
var increwvariance = require( '@stdlib/stats/incr/ewvariance' );

var accumulator;
var v;
var i;

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

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

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See Also

• @stdlib/stats/incr/ewmean: compute an exponentially weighted mean incrementally.
• @stdlib/stats/incr/ewstdev: compute an exponentially weighted standard deviation incrementally.
• @stdlib/stats/incr/variance: compute an unbiased sample variance incrementally.
• @stdlib/stats/incr/mvariance: compute a moving unbiased sample variance incrementally.