incrmmeanvar

Compute a moving arithmetic mean and unbiased sample variance incrementally.

For a window of size W, 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

and 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 incrmmeanvar = require( '@stdlib/stats/incr/mmeanvar' );

incrmmeanvar( [out,] window )

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

var accumulator = incrmmeanvar( 3 );

By default, the returned accumulator function returns the accumulated values as a two-element array. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.

var Float64Array = require( '@stdlib/array/float64' );

var accumulator = incrmmeanvar( new Float64Array( 2 ), 3 );

accumulator( [x] )

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

var accumulator = incrmmeanvar( 3 );

var out = accumulator();
// returns null

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

out = accumulator( 1.0 ); // [2.0, 1.0]
// returns [ 1.5, 0.5 ]

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

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

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

out = accumulator();
// returns [ -3.0, 28.0 ]

Notes

  • Input values are not type checked. If provided NaN, the accumulated values are 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 Float64Array = require( '@stdlib/array/float64' );
var ArrayBuffer = require( '@stdlib/array/buffer' );
var incrmmeanvar = require( '@stdlib/stats/incr/mmeanvar' );

var offset;
var acc;
var buf;
var out;
var mv;
var N;
var v;
var i;
var j;

// Define the number of accumulators:
N = 5;

// Create an array buffer for storing accumulator output:
buf = new ArrayBuffer( N*2*8 ); // 8 bytes per element

// Initialize accumulators:
acc = [];
for ( i = 0; i < N; i++ ) {
    // Compute the byte offset:
    offset = i * 2 * 8; // stride=2, bytes_per_element=8

    // Create a new view for storing accumulated values:
    out = new Float64Array( buf, offset, 2 );

    // Initialize an accumulator which will write results to the view:
    acc.push( incrmmeanvar( out, 5 ) );
}

// Simulate data and update the moving sample means and variances...
for ( i = 0; i < 100; i++ ) {
    for ( j = 0; j < N; j++ ) {
        v = randu() * 100.0 * (j+1);
        acc[ j ]( v );
    }
}

// Print the final results:
console.log( 'Mean\tVariance' );
for ( i = 0; i < N; i++ ) {
    mv = acc[ i ]();
    console.log( '%d\t%d', mv[ 0 ].toFixed( 3 ), mv[ 1 ].toFixed( 3 ) );
}