Compute a moving sum incrementally.

stdlib, stdmath, statistics, stats, mathematics, math, sum, total, incremental, accumulator, moving sum, sliding window, sliding, window, moving, javascript, moving-sum, node, node-js, nodejs, sliding-window
npm install @stdlib/stats-incr-msum@0.0.5



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Compute a moving sum incrementally.

For a window of size W, the moving sum is defined as

Equation for the moving sum.


npm install @stdlib/stats-incr-msum


var incrmsum = require( '@stdlib/stats-incr-msum' );

incrmsum( window )

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

var accumulator = incrmsum( 3 );

accumulator( [x] )

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

var accumulator = incrmsum( 3 );

var sum = accumulator();
// returns null

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

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

sum = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns 6.0

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

sum = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns -9.0

sum = accumulator();
// returns -9.0


  • 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.


var randu = require( '@stdlib/random-base-randu' );
var incrmsum = require( '@stdlib/stats-incr-msum' );

var accumulator;
var v;
var i;

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

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


This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.






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