npm package: @stdlib/stats-strided-dmeanstdevpn
Description: Calculate the mean and standard deviation of a double-precision floating-point strided array using a two-pass algorithm.
Author: The Stdlib Authors
Latest version: 0.1.1

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# dmeanstdevpn

[![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 [mean][arithmetic-mean] and [standard deviation][standard-deviation] of a double-precision floating-point strided array using a two-pass algorithm.

<section class="intro">

The population [standard deviation][standard-deviation] of a finite size population of size `N` is given by

<!-- <equation class="equation" label="eq:population_standard_deviation" align="center" raw="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" alt="Equation for the population standard deviation."> -->

<div class="equation" align="center" data-raw-text="\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}" data-equation="eq:population_standard_deviation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8467ec3de1244d48205fbf95404ac53f957b4c5b/lib/node_modules/@stdlib/stats/strided/dmeanstdevpn/docs/img/equation_population_standard_deviation.svg" alt="Equation for the population standard deviation.">
    <br>
</div> -->

<!-- </equation> -->

where the population mean is given by

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

<!-- <div class="equation" align="center" data-raw-text="\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i" data-equation="eq:population_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8467ec3de1244d48205fbf95404ac53f957b4c5b/lib/node_modules/@stdlib/stats/strided/dmeanstdevpn/docs/img/equation_population_mean.svg" alt="Equation for the population mean.">
    <br>
</div> -->

<!-- </equation> -->

Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. If one attempts to use the formula for the population [standard deviation][standard-deviation], the result is biased and yields an **uncorrected sample standard deviation**. To compute a **corrected sample standard deviation** for a sample of size `n`,

<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" alt="Equation for computing a corrected sample standard deviation."> -->

<!-- <div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}" data-equation="eq:corrected_sample_standard_deviation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8467ec3de1244d48205fbf95404ac53f957b4c5b/lib/node_modules/@stdlib/stats/strided/dmeanstdevpn/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for computing a corrected sample standard deviation.">
    <br>
</div> -->

<!-- </equation> -->

where the sample mean is given by

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

<!-- <div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" data-equation="eq:sample_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@8467ec3de1244d48205fbf95404ac53f957b4c5b/lib/node_modules/@stdlib/stats/strided/dmeanstdevpn/docs/img/equation_sample_mean.svg" alt="Equation for the sample mean.">
    <br>
</div>

<!-- </equation> -->

The use of the term `n-1` is commonly referred to as Bessel's correction. Note, however, that applying Bessel's correction can increase the mean squared error between the sample standard deviation and population standard deviation. Depending on the characteristics of the population distribution, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-strided-dmeanstdevpn
```

</section>

<section class="usage">

## Usage

```javascript
var dmeanstdevpn = require( '@stdlib/stats-strided-dmeanstdevpn' );
```

#### dmeanstdevpn( N, correction, x, strideX, out, strideOut )

Computes the [mean][arithmetic-mean] and [standard deviation][standard-deviation] of a double-precision floating-point strided array using a two-pass algorithm.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var out = new Float64Array( 2 );

var v = dmeanstdevpn( x.length, 1, x, 1, out, 1 );
// returns <Float64Array>[ ~0.3333, ~2.0817 ]

var bool = ( v === out );
// returns true
```

The function has the following parameters:

-   **N**: number of indexed elements.
-   **correction**: degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample [standard deviation][standard-deviation], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
-   **x**: input [`Float64Array`][@stdlib/array/float64].
-   **strideX**: stride length for `x`.
-   **out**: output [`Float64Array`][@stdlib/array/float64] for storing results.
-   **strideOut**: stride length for `out`.

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

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

var x = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
var out = new Float64Array( 2 );

var v = dmeanstdevpn( 4, 1, x, 2, out, 1 );
// returns <Float64Array>[ 1.25, 2.5 ]
```

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 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 out0 = new Float64Array( 4 );
var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

var v = dmeanstdevpn( 4, 1, x1, 2, out1, 1 );
// returns <Float64Array>[ 1.25, 2.5 ]
```

#### dmeanstdevpn.ndarray( N, correction, x, strideX, offsetX, out, strideOut, offsetOut )

Computes the [mean][arithmetic-mean] and [standard deviation][standard-deviation] of a double-precision floating-point strided array using a two-pass algorithm and alternative indexing semantics.

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

var x = new Float64Array( [ 1.0, -2.0, 2.0 ] );
var out = new Float64Array( 2 );

var v = dmeanstdevpn.ndarray( x.length, 1, x, 1, 0, out, 1, 0 );
// returns <Float64Array>[ ~0.3333, ~2.0817 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.
-   **offsetOut**: starting index for `out`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to calculate the [mean][arithmetic-mean] and [standard deviation][standard-deviation] for every other element in `x` starting from the second element

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

var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var out = new Float64Array( 4 );

var v = dmeanstdevpn.ndarray( 4, 1, x, 2, 1, out, 2, 1 );
// returns <Float64Array>[ 0.0, 1.25, 0.0, 2.5 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `N <= 0`, both functions return a [mean][arithmetic-mean] and [standard deviation][standard-deviation] equal to `NaN`.
-   If `N - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment), both functions return a [standard deviation][standard-deviation] equal to `NaN`.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Float64Array = require( '@stdlib/array-float64' );
var dmeanstdevpn = require( '@stdlib/stats-strided-dmeanstdevpn' );

var x = discreteUniform( 10, -50, 50, {
    'dtype': 'float64'
});
console.log( x );

var out = new Float64Array( 2 );
dmeanstdevpn( x.length, 1, x, 1, out, 1 );
console.log( out );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/strided/dmeanstdevpn.h"
```

#### stdlib_strided_dmeanstdevpn( N, correction, \*X, strideX, \*Out, strideOut )

Computes the [mean][arithmetic-mean] and [standard deviation][standard-deviation] of a double-precision floating-point strided array using a two-pass algorithm.

```c
const double x[] = { 1.0, -2.0, 2.0 };
double out[] = { 0.0, 0.0 };

stdlib_strided_dmeanstdevpn( 3, 1.0, x, 1, out, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **correction**: `[in] double` degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample [standard deviation][standard-deviation], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
-   **X**: `[in] double*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **Out**: `[out] double*` output array.
-   **strideOut**: `[in] CBLAS_INT` stride length for `Out`.

```c
void stdlib_strided_dmeanstdevpn( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX, double *Out, const CBLAS_INT strideOut );
```

#### stdlib_strided_dmeanstdevpn_ndarray( N, correction, \*X, strideX, offsetX, \*Out, strideOut, offsetOut )

Computes the [mean][arithmetic-mean] and [standard deviation][standard-deviation] of a double-precision floating-point strided array using a two-pass algorithm and alternative indexing semantics.

```c
const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
double out[] = { 0.0, 0.0 };

stdlib_strided_dmeanstdevpn_ndarray( 4, 1.0, x, 2, 0, x, 1, 0 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **correction**: `[in] double` degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [standard deviation][standard-deviation] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the [standard deviation][standard-deviation] of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample [standard deviation][standard-deviation], setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel's correction).
-   **X**: `[in] double*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
-   **Out**: `[out] double*` output array.
-   **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
-   **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.

```c
void stdlib_strided_dmeanstdevpn_ndarray( const CBLAS_INT N, const double correction, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Out, const CBLAS_INT strideOut, const CBLAS_INT offsetOut );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/strided/dmeanstdevpn.h"
#include <stdio.h>

int main( void ) {
    // Create a strided array:
    const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };

    // Create an output array:
    double out[] = { 0.0, 0.0 };

    // Specify the number of elements:
    const int N = 4;

    // Specify the stride length:
    const int strideX = 2;
    const int strideOut = 1;

    // Compute the mean and standard deviation:
    stdlib_strided_dmeanstdevpn( N, 1.0, x, strideX, out, strideOut );

    // Print the result:
    printf( "sample mean: %lf\n", out[ 0 ] );
    printf( "sample standard deviation: %lf\n", out[ 1 ] );
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<section class="references">

## References

-   Neely, Peter M. 1966. "Comparison of Several Algorithms for Computation of Means, Standard Deviations and Correlation Coefficients." _Communications of the ACM_ 9 (7). Association for Computing Machinery: 496–99. doi:[10.1145/365719.365958][@neely:1966a].
-   Schubert, Erich, and Michael Gertz. 2018. "Numerically Stable Parallel Computation of (Co-)Variance." In _Proceedings of the 30th International Conference on Scientific and Statistical Database Management_. New York, NY, USA: Association for Computing Machinery. doi:[10.1145/3221269.3223036][@schubert:2018a].

</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-strided/dmeanpn`][@stdlib/stats/strided/dmeanpn]</span><span class="delimiter">: </span><span class="description">calculate the arithmetic mean of a double-precision floating-point strided array using a two-pass error correction algorithm.</span>
-   <span class="package-name">[`@stdlib/stats-strided/dmeanstdev`][@stdlib/stats/strided/dmeanstdev]</span><span class="delimiter">: </span><span class="description">calculate the mean and standard deviation of a double-precision floating-point strided array.</span>
-   <span class="package-name">[`@stdlib/stats-strided/dmeanvarpn`][@stdlib/stats/strided/dmeanvarpn]</span><span class="delimiter">: </span><span class="description">calculate the mean and variance of a double-precision floating-point strided array using a two-pass algorithm.</span>
-   <span class="package-name">[`@stdlib/stats-strided/dstdevpn`][@stdlib/stats/strided/dstdevpn]</span><span class="delimiter">: </span><span class="description">calculate the standard deviation of a double-precision floating-point strided array using a two-pass algorithm.</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; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[umd]: https://github.com/umdjs/umd
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[deno-url]: https://github.com/stdlib-js/stats-strided-dmeanstdevpn/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-strided-dmeanstdevpn/blob/deno/README.md
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-strided-dmeanstdevpn/main/LICENSE

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

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

[@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

[@neely:1966a]: https://doi.org/10.1145/365719.365958

[@schubert:2018a]: https://doi.org/10.1145/3221269.3223036

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[@stdlib/stats/strided/dmeanvarpn]: https://www.npmjs.com/package/@stdlib/stats-strided-dmeanvarpn

[@stdlib/stats/strided/dstdevpn]: https://www.npmjs.com/package/@stdlib/stats-strided-dstdevpn

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</section>

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