npm package: @stdlib/stats-base-dmeanlipw
Description: Calculate the arithmetic mean of a double-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.
Author: The Stdlib Authors
Latest version: 0.2.2

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<details>
  <summary>
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# dmeanlipw

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Calculate the [arithmetic mean][arithmetic-mean] of a double-precision floating-point strided array using a one-pass trial mean algorithm with pairwise 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@4415a930fcdcfd8c5ff6a8781a93d88b40ab0e18/lib/node_modules/@stdlib/stats/base/dmeanlipw/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dmeanlipw
```

</section>

<section class="usage">

## Usage

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

#### dmeanlipw( N, x, stride )

Computes the [arithmetic mean][arithmetic-mean] of a double-precision floating-point strided array `x` using a one-pass trial mean algorithm with pairwise summation.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

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

The function has the following parameters:

-   **N**: number of indexed elements.
-   **x**: input [`Float64Array`][@stdlib/array/float64].
-   **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 Float64Array = require( '@stdlib/array-float64' );
var floor = require( '@stdlib/math-base-special-floor' );

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var N = floor( x.length / 2 );

var v = dmeanlipw( 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 ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

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

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

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

Computes the [arithmetic mean][arithmetic-mean] of a double-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation and alternative indexing semantics.

```javascript
var Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = dmeanlipw.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 Float64Array = require( '@stdlib/array-float64' );
var floor = require( '@stdlib/math-base-special-floor' );

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );

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

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return `NaN`.
-   The underlying algorithm is a specialized case of Welford's algorithm. Similar to the method of assumed mean, the first strided array element is used as a trial mean. The trial mean is subtracted from subsequent data values, and the average deviations used to adjust the initial guess. Accordingly, the algorithm's accuracy is best when data is **unordered** (i.e., the data is **not** sorted in either ascending or descending order such that the first value is an "extreme" value).

</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 dmeanlipw = require( '@stdlib/stats-base-dmeanlipw' );

var x;
var i;

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

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

</section>

<!-- /.examples -->

* * *

<section class="references">

## References

-   Welford, B. P. 1962. "Note on a Method for Calculating Corrected Sums of Squares and Products." _Technometrics_ 4 (3). Taylor & Francis: 419–20. doi:[10.1080/00401706.1962.10490022][@welford:1962a].
-   van Reeken, A. J. 1968. "Letters to the Editor: Dealing with Neely's Algorithms." _Communications of the ACM_ 11 (3): 149–50. doi:[10.1145/362929.362961][@vanreeken:1968a].
-   Ling, Robert F. 1974. "Comparison of Several Algorithms for Computing Sample Means and Variances." _Journal of the American Statistical Association_ 69 (348). American Statistical Association, Taylor & Francis, Ltd.: 859–66. doi:[10.2307/2286154][@ling:1974a].
-   Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050][@higham:1993a].

</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/dmean`][@stdlib/stats/base/dmean]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a double-precision floating-point strided array.</span>
-   <span class="package-name">[`@stdlib/stats-base/dmeanli`][@stdlib/stats/base/dmeanli]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a double-precision floating-point strided array using a one-pass trial mean algorithm.</span>
-   <span class="package-name">[`@stdlib/stats-base/dmeanpw`][@stdlib/stats/base/dmeanpw]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a double-precision floating-point strided array using pairwise summation.</span>
-   <span class="package-name">[`@stdlib/stats-base/smeanlipw`][@stdlib/stats/base/smeanlipw]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a single-precision floating-point strided array using a one-pass trial mean algorithm with pairwise summation.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## 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 &copy; 2016-2024. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[esm-url]: https://github.com/stdlib-js/stats-base-dmeanlipw/tree/esm
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dmeanlipw/main/LICENSE

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

[@stdlib/array/float64]: https://www.npmjs.com/package/@stdlib/array-float64

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

[@welford:1962a]: https://doi.org/10.1080/00401706.1962.10490022

[@vanreeken:1968a]: https://doi.org/10.1145/362929.362961

[@ling:1974a]: https://doi.org/10.2307/2286154

[@higham:1993a]: https://doi.org/10.1137/0914050

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

[@stdlib/stats/base/dmean]: https://www.npmjs.com/package/@stdlib/stats-base-dmean

[@stdlib/stats/base/dmeanli]: https://www.npmjs.com/package/@stdlib/stats-base-dmeanli

[@stdlib/stats/base/dmeanpw]: https://www.npmjs.com/package/@stdlib/stats-base-dmeanpw

[@stdlib/stats/base/smeanlipw]: https://www.npmjs.com/package/@stdlib/stats-base-smeanlipw

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</section>

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