@stdlib/stats/base/nanmeanors/README.md

Standard library statistical functions.

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# nanmeanors

> Calculate the [arithmetic mean][arithmetic-mean] of a strided array, ignoring `NaN` values and using ordinary recursive summation.

<section class="intro">

The [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\mu = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:arithmetic_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@9175c13dbc0434906c9644e01a0c6d2f700fc087/lib/node_modules/@stdlib/stats/base/nanmeanors/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var nanmeanors = require( '@stdlib/stats/base/nanmeanors' );
```

#### nanmeanors( N, x, stride )

Computes the [arithmetic mean][arithmetic-mean] of a strided array `x`, ignoring `NaN` values and using ordinary recursive summation.

```javascript
var x = [ 1.0, -2.0, NaN, 2.0 ];
var N = x.length;

var v = nanmeanors( N, x, 1 );
// returns ~0.3333
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **stride**: index increment for `x`.

The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [arithmetic mean][arithmetic-mean] of every other element in `x`,

```javascript
var floor = require( '@stdlib/math/base/special/floor' );

var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0, NaN ];
var N = floor( x.length / 2 );

var v = nanmeanors( N, x, 2 );
// returns 1.25
```

Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.

<!-- eslint-disable stdlib/capitalized-comments -->

```javascript
var Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );

var x0 = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var N = floor( x0.length / 2 );

var v = nanmeanors( N, x1, 2 );
// returns 1.25
```

#### nanmeanors.ndarray( N, x, stride, offset )

Computes the [arithmetic mean][arithmetic-mean] of a strided array, ignoring `NaN` values and using ordinary recursive summation and alternative indexing semantics.

```javascript
var x = [ 1.0, -2.0, NaN, 2.0 ];
var N = x.length;

var v = nanmeanors.ndarray( N, x, 1, 0 );
// returns ~0.33333
```

The function has the following additional parameters:

-   **offset**: starting index for `x`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying `buffer`, the `offset` parameter supports indexing semantics based on a starting index. For example, to calculate the [arithmetic mean][arithmetic-mean] for every other value in `x` starting from the second value

```javascript
var floor = require( '@stdlib/math/base/special/floor' );

var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN ];
var N = floor( x.length / 2 );

var v = nanmeanors.ndarray( N, x, 2, 1 );
// returns 1.25
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `NaN`.
-   If every indexed element is `NaN`, both functions return `NaN`.
-   Ordinary recursive summation (i.e., a "simple" sum) is performant, but can incur significant numerical error. If performance is paramount and error tolerated, using ordinary recursive summation to compute an arithmetic mean is acceptable; in all other cases, exercise due caution.
-   Depending on the environment, the typed versions ([`dnanmeanors`][@stdlib/stats/base/dnanmeanors], [`snanmeanors`][@stdlib/stats/base/snanmeanors], etc.) are likely to be significantly more performant.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var nanmeanors = require( '@stdlib/stats/base/nanmeanors' );

var x;
var i;

x = new Float64Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    if ( randu() < 0.2 ) {
        x[ i ] = NaN;
    } else {
        x[ i ] = round( (randu()*100.0) - 50.0 );
    }
}
console.log( x );

var v = nanmeanors( x.length, x, 1 );
console.log( v );
```

</section>

<!-- /.examples -->

<section class="references">

</section>

<!-- /.references -->

<!-- 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/base/dnanmeanors`][@stdlib/stats/base/dnanmeanors]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a double-precision floating-point strided array, ignoring NaN values and using ordinary recursive summation.</span>
-   <span class="package-name">[`@stdlib/stats/base/meanors`][@stdlib/stats/base/meanors]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a strided array using ordinary recursive summation.</span>
-   <span class="package-name">[`@stdlib/stats/base/nanmean`][@stdlib/stats/base/nanmean]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a strided array, ignoring NaN values.</span>
-   <span class="package-name">[`@stdlib/stats/base/snanmeanors`][@stdlib/stats/base/snanmeanors]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a single-precision floating-point strided array, ignoring NaN values and using ordinary recursive summation.</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">

[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean

[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

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

[@stdlib/stats/base/dnanmeanors]: https://github.com/stdlib-js/stats/tree/main/base/dnanmeanors

[@stdlib/stats/base/meanors]: https://github.com/stdlib-js/stats/tree/main/base/meanors

[@stdlib/stats/base/nanmean]: https://github.com/stdlib-js/stats/tree/main/base/nanmean

[@stdlib/stats/base/snanmeanors]: https://github.com/stdlib-js/stats/tree/main/base/snanmeanors

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

</section>

<!-- /.links -->