incrmvariance

Compute a moving unbiased sample variance incrementally.

For a window of size W, the unbiased sample variance is defined as

s squared equals 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

Usage

var incrmvariance = require( '@stdlib/stats/incr/mvariance' );

incrmvariance( window[, mean] )

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

var accumulator = incrmvariance( 3 );

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

var accumulator = incrmvariance( 3, 5.0 );

accumulator( [x] )

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

var accumulator = incrmvariance( 3 );

var s2 = accumulator();
// returns null

// Fill the window...
s2 = accumulator( 2.0 ); // [2.0]
// returns 0.0

s2 = accumulator( 1.0 ); // [2.0, 1.0]
// returns 0.5

s2 = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns 1.0

// Window begins sliding...
s2 = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns 28.0

s2 = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns 28.0

s2 = accumulator();
// returns 28.0

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 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.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrmvariance = require( '@stdlib/stats/incr/mvariance' );

var accumulator;
var v;
var i;

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

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