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increwstdev

Compute an exponentially weighted standard deviation 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. The exponentially weighted standard deviation is the square root of the exponentially weighted variance.

Installation

npm install @stdlib/stats-incr-ewstdev

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var increwstdev = require( '@stdlib/stats-incr-ewstdev' );

increwstdev( alpha )

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

var accumulator = increwstdev( 0.5 );

accumulator( [x] )

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

var accumulator = increwstdev( 0.5 );

var s = accumulator();
// returns null

s = accumulator( 2.0 );
// returns 0.0

s = accumulator( 1.0 );
// returns 0.5

s = accumulator( 3.0 );
// returns ~0.83

s = accumulator();
// returns ~0.83

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 increwstdev = require( '@stdlib/stats-incr-ewstdev' );

var accumulator;
var v;
var i;

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

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

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See Also

• @stdlib/stats-incr/ewvariance: compute an exponentially weighted variance incrementally.
• @stdlib/stats-incr/mstdev: compute a moving corrected sample standard deviation incrementally.
• @stdlib/stats-incr/stdev: compute a corrected sample standard deviation incrementally.

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Notice

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.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.