https://github.com/stdlib-js/stats-incr-mmaape
Compute a moving arctangent mean absolute percentage error (MAAPE) incrementally.
https://github.com/stdlib-js/stats-incr-mmaape
abs absolute accumulator average avg err error incremental javascript maape mape math mathematics mean node node-js nodejs statistics stats stdlib
Last synced: 6 months ago
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Compute a moving arctangent mean absolute percentage error (MAAPE) incrementally.
- Host: GitHub
- URL: https://github.com/stdlib-js/stats-incr-mmaape
- Owner: stdlib-js
- License: apache-2.0
- Created: 2021-06-15T16:15:55.000Z (over 4 years ago)
- Default Branch: main
- Last Pushed: 2025-03-17T00:55:27.000Z (7 months ago)
- Last Synced: 2025-04-12T17:43:30.851Z (6 months ago)
- Topics: abs, absolute, accumulator, average, avg, err, error, incremental, javascript, maape, mape, math, mathematics, mean, node, node-js, nodejs, statistics, stats, stdlib
- Language: JavaScript
- Homepage: https://github.com/stdlib-js/stdlib
- Size: 937 KB
- Stars: 2
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff
- Security: SECURITY.md
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README
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# incrmmaape
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Compute a moving [mean arctangent absolute percentage error][@kim:2016a] (MAAPE) incrementally.
For a window of size `W`, the [mean arctangent absolute percentage error][@kim:2016a] is defined as
```math
\mathop{\mathrm{MAAPE}} = \frac{1}{W} \sum_{i=0}^{W-1} \mathop{\mathrm{arctan}}\biggl( \biggl| \frac{a_i - f_i}{a_i} \biggr| \biggr)
```
where `f_i` is the forecast value and `a_i` is the actual value.
## Installation
```bash
npm install @stdlib/stats-incr-mmaape
```
Alternatively,
- To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).
The [branches.md][branches-url] 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
```javascript
var incrmmaape = require( '@stdlib/stats-incr-mmaape' );
```
#### incrmmaape( window )
Returns an accumulator `function` which incrementally computes a moving [mean arctangent absolute percentage error][@kim:2016a]. The `window` parameter defines the number of values over which to compute the moving [mean arctangent absolute percentage error][@kim:2016a].
```javascript
var accumulator = incrmmaape( 3 );
```
#### accumulator( \[f, a] )
If provided input values `f` and `a`, the accumulator function returns an updated [mean arctangent absolute percentage error][@kim:2016a]. If not provided input values `f` and `a`, the accumulator function returns the current [mean arctangent absolute percentage error][@kim:2016a].
```javascript
var accumulator = incrmmaape( 3 );
var m = accumulator();
// returns null
// Fill the window...
m = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns ~0.32
m = accumulator( 1.0, 4.0 ); // [(2.0,3.0), (1.0,4.0)]
// returns ~0.48
m = accumulator( 3.0, 9.0 ); // [(2.0,3.0), (1.0,4.0), (3.0,9.0)]
// returns ~0.52
// Window begins sliding...
m = accumulator( 7.0, 3.0 ); // [(1.0,4.0), (3.0,9.0), (7.0,3.0)]
// returns ~0.72
m = accumulator( 5.0, 3.0 ); // [(3.0,9.0), (7.0,3.0), (5.0,3.0)]
// returns ~0.70
m = accumulator();
// returns ~0.70
```
## 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` (f,a) pairs 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.
- Note that, unlike the [mean absolute percentage error][@stdlib/stats/incr/mape] (MAPE), the [mean arctangent absolute percentage error][@kim:2016a] is expressed in radians on the interval \[0,π/2].
## Examples
```javascript
var randu = require( '@stdlib/random-base-randu' );
var incrmmaape = require( '@stdlib/stats-incr-mmaape' );
var accumulator;
var v1;
var v2;
var i;
// Initialize an accumulator:
accumulator = incrmmaape( 5 );
// For each simulated datum, update the moving mean arctangent absolute percentage error...
for ( i = 0; i < 100; i++ ) {
v1 = ( randu()*100.0 ) + 50.0;
v2 = ( randu()*100.0 ) + 50.0;
accumulator( v1, v2 );
}
console.log( accumulator() );
```
## References
- Kim, Sungil, and Heeyoung Kim. 2016. "A new metric of absolute percentage error for intermittent demand forecasts." _International Journal of Forecasting_ 32 (3): 669–79. doi:[10.1016/j.ijforecast.2015.12.003][@kim:2016a].
* * *
## See Also
- [`@stdlib/stats-incr/maape`][@stdlib/stats/incr/maape]: compute the mean arctangent absolute percentage error (MAAPE) incrementally.
- [`@stdlib/stats-incr/mmape`][@stdlib/stats/incr/mmape]: compute a moving mean absolute percentage error (MAPE) incrementally.
- [`@stdlib/stats-incr/mmpe`][@stdlib/stats/incr/mmpe]: compute a moving mean percentage error (MPE) incrementally.
- [`@stdlib/stats-incr/mmean`][@stdlib/stats/incr/mmean]: compute a moving arithmetic mean incrementally.
* * *
## Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
## License
See [LICENSE][stdlib-license].
## Copyright
Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-incr-mmaape.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-incr-mmaape
[test-image]: https://github.com/stdlib-js/stats-incr-mmaape/actions/workflows/test.yml/badge.svg?branch=main
[test-url]: https://github.com/stdlib-js/stats-incr-mmaape/actions/workflows/test.yml?query=branch:main
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-incr-mmaape/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-incr-mmaape?branch=main
[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg
[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-incr-mmaape/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-incr-mmaape/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-incr-mmaape/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-incr-mmaape/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-incr-mmaape/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-incr-mmaape/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-incr-mmaape/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-mmaape/main/LICENSE
[@kim:2016a]: https://www.sciencedirect.com/science/article/pii/S0169207016000121
[@stdlib/stats/incr/mape]: https://github.com/stdlib-js/stats-incr-mape
[@stdlib/stats/incr/maape]: https://github.com/stdlib-js/stats-incr-maape
[@stdlib/stats/incr/mmape]: https://github.com/stdlib-js/stats-incr-mmape
[@stdlib/stats/incr/mmpe]: https://github.com/stdlib-js/stats-incr-mmpe
[@stdlib/stats/incr/mmean]: https://github.com/stdlib-js/stats-incr-mmean