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# incrhmean

> Compute a [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{\displaystyle n}{\displaystyle\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle\sum_{i=0}^{n-1} \frac{1}{x_i}}{\displaystyle n} \biggr)^{-1}\end{align}" alt="Equation for the harmonic mean."> -->

<div class="equation" align="center" data-raw-text="\begin{align}H &amp;= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &amp;= \frac{\displaystyle n}{\displaystyle\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &amp;= \biggl( \frac{\displaystyle\sum_{i=0}^{n-1} \frac{1}{x_i}}{\displaystyle n} \biggr)^{-1}\end{align}" data-equation="eq:harmonic_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@2b632747053b9e357a4663369528fe62b29a6d55/lib/node_modules/@stdlib/stats/incr/hmean/docs/img/equation_harmonic_mean.svg" alt="Equation for the harmonic mean.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrhmean = require( '@stdlib/stats/incr/hmean' );
```

#### incrhmean()

Returns an accumulator `function` which incrementally computes a [harmonic mean][harmonic-mean].

```javascript
var accumulator = incrhmean();
```

#### 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 = incrhmean();

var v = accumulator( 2.0 );
// returns 2.0

v = accumulator( 1.0 );
// returns ~1.33

v = accumulator( 3.0 );
// returns ~1.64

v = accumulator();
// returns ~1.64
```

</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 **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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrhmean = require( '@stdlib/stats/incr/hmean' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrhmean();

// For each simulated datum, update the 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/gmean`][@stdlib/stats/incr/gmean]</span><span class="delimiter">: </span><span class="description">compute a geometric mean incrementally.</span>
-   <span class="package-name">[`@stdlib/stats/incr/mean`][@stdlib/stats/incr/mean]</span><span class="delimiter">: </span><span class="description">compute an arithmetic mean incrementally.</span>
-   <span class="package-name">[`@stdlib/stats/incr/mhmean`][@stdlib/stats/incr/mhmean]</span><span class="delimiter">: </span><span class="description">compute a moving harmonic mean incrementally.</span>
-   <span class="package-name">[`@stdlib/stats/incr/summary`][@stdlib/stats/incr/summary]</span><span class="delimiter">: </span><span class="description">compute a statistical summary 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/gmean]: https://github.com/stdlib-js/stats/tree/main/incr/gmean

[@stdlib/stats/incr/mean]: https://github.com/stdlib-js/stats/tree/main/incr/mean

[@stdlib/stats/incr/mhmean]: https://github.com/stdlib-js/stats/tree/main/incr/mhmean

[@stdlib/stats/incr/summary]: https://github.com/stdlib-js/stats/tree/main/incr/summary

<!-- </related-links> -->

</section>

<!-- /.links -->
