# incrmmeanstdev

Compute a moving arithmetic mean and corrected sample standard deviation incrementally.

For a window of size W, the arithmetic mean is defined as

and the corrected sample standard deviation is defined as

## Usage

var incrmmeanstdev = require( '@stdlib/stats/incr/mmeanstdev' );


#### incrmmeanstdev( [out,] window )

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

var accumulator = incrmmeanstdev( 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 = incrmmeanstdev( 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 = incrmmeanstdev( 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, ~0.71 ]

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, ~5.29 ]

out = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns [ -3.0, ~5.29 ]

out = accumulator();
// returns [ -3.0, ~5.29 ]


## 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 incrmmeanstdev = require( '@stdlib/stats/incr/mmeanstdev' );

var offset;
var acc;
var buf;
var out;
var ms;
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( incrmmeanstdev( out, 5 ) );
}

// Simulate data and update the moving sample means and standard deviations...
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\tStDev' );
for ( i = 0; i < N; i++ ) {
ms = acc[ i ]();
console.log( '%d\t%d', ms[ 0 ].toFixed( 3 ), ms[ 1 ].toFixed( 3 ) );
}