@stdlib/stats
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Standard library statistical functions.
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# incrmhmean
> Compute a moving [harmonic mean][harmonic-mean] incrementally.
<section class="intro">
The [harmonic mean][harmonic-mean] of positive real numbers `x_0, x_1, ..., x_{n-1}` is defined as
<!-- <equation class="equation" label="eq:harmonic_mean" align="center" raw="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\displaystyle\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" alt="Equation for the harmonic mean."> -->
<div class="equation" align="center" data-raw-text="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\displaystyle\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle \sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" data-equation="eq:harmonic_mean">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0a561712608b99b59d9243f7d478a2e2a019a130/lib/node_modules/@stdlib/stats/incr/mhmean/docs/img/equation_harmonic_mean.svg" alt="Equation for the harmonic mean.">
<br>
</div>
<!-- </equation> -->
</section>
<!-- /.intro -->
<section class="usage">
## Usage
```javascript
var incrmhmean = require( '@stdlib/stats/incr/mhmean' );
```
#### incrmhmean( window )
Returns an accumulator `function` which incrementally computes a moving [harmonic mean][harmonic-mean]. The `window` parameter defines the number of values over which to compute the moving [harmonic mean][harmonic-mean].
```javascript
var accumulator = incrmhmean( 3 );
```
#### accumulator( \[x] )
If provided an input value `x`, the accumulator function returns an updated [harmonic mean][harmonic-mean]. If not provided an input value `x`, the accumulator function returns the current [harmonic-mean][harmonic-mean].
```javascript
var accumulator = incrmhmean( 3 );
var v = accumulator();
// returns null
// Fill the window...
v = accumulator( 2.0 ); // [2.0]
// returns 2.0
v = accumulator( 1.0 ); // [2.0, 1.0]
// returns ~1.33
v = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns ~1.64
// Window begins sliding...
v = accumulator( 7.0 ); // [1.0, 3.0, 7.0]
// returns ~2.03
v = accumulator( 5.0 ); // [3.0, 7.0, 5.0]
// returns ~4.44
v = accumulator();
// returns ~4.44
```
</section>
<!-- /.usage -->
<section class="notes">
## 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` 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.
</section>
<!-- /.notes -->
<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmhmean = require( '@stdlib/stats/incr/mhmean' );
var accumulator;
var v;
var i;
// Initialize an accumulator:
accumulator = incrmhmean( 5 );
// For each simulated datum, update the moving harmonic mean...
for ( i = 0; i < 100; i++ ) {
v = randu() * 100.0;
accumulator( v );
}
console.log( accumulator() );
```
</section>
<!-- /.examples -->
<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
<section class="related">
* * *
## See Also
- <span class="package-name">[`@stdlib/stats/incr/hmean`][@stdlib/stats/incr/hmean]</span><span class="delimiter">: </span><span class="description">compute a harmonic mean incrementally.</span>
- <span class="package-name">[`@stdlib/stats/incr/mgmean`][@stdlib/stats/incr/mgmean]</span><span class="delimiter">: </span><span class="description">compute a moving geometric mean incrementally.</span>
- <span class="package-name">[`@stdlib/stats/incr/mmean`][@stdlib/stats/incr/mmean]</span><span class="delimiter">: </span><span class="description">compute a moving arithmetic mean incrementally.</span>
</section>
<!-- /.related -->
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
<section class="links">
[harmonic-mean]: https://en.wikipedia.org/wiki/Harmonic_mean
<!-- <related-links> -->
[@stdlib/stats/incr/hmean]: https://github.com/stdlib-js/stats/tree/main/incr/hmean
[@stdlib/stats/incr/mgmean]: https://github.com/stdlib-js/stats/tree/main/incr/mgmean
[@stdlib/stats/incr/mmean]: https://github.com/stdlib-js/stats/tree/main/incr/mmean
<!-- </related-links> -->
</section>
<!-- /.links -->