@stdlib/stats-base-nanstdevtk

Calculate the standard deviation of a strided array ignoring NaN values and using a one-pass textbook algorithm.

https://github.com/stdlib-js/stats-base-nanstdevtk

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array deviation dispersion javascript math mathematics node node-js nodejs sample-standard-deviation standard-deviation statistics stats stdlib strided strided-array typed unbiased var variance

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Calculate the standard deviation of a strided array ignoring NaN values and using a one-pass textbook algorithm.

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Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
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array deviation dispersion javascript math mathematics node node-js nodejs sample-standard-deviation standard-deviation statistics stats stdlib strided strided-array typed unbiased var variance

Created over 4 years ago · Last pushed 5 months ago

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We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

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To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

nanstdevtk

Calculate the standard deviation of a strided array ignoring NaN values and using a one-pass textbook algorithm.

The population [standard deviation][standard-deviation] of a finite size population of size `N` is given by ```math \sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2} ``` where the population mean is given by ```math \mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i ``` 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`, ```math s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2} ``` where the sample mean is given by ```math \bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i ``` 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.

## Installation ```bash npm install @stdlib/stats-base-nanstdevtk ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships. To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## Usage ```javascript var nanstdevtk = require( '@stdlib/stats-base-nanstdevtk' ); ``` #### nanstdevtk( N, correction, x, strideX ) Computes the [standard deviation][standard-deviation] of a strided array ignoring `NaN` values and using a one-pass textbook algorithm. ```javascript var x = [ 1.0, -2.0, NaN, 2.0 ]; var v = nanstdevtk( x.length, 1, x, 1 ); // returns ~2.0817 ``` 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 [`Array`][mdn-array] or [`typed array`][mdn-typed-array]. - **strideX**: stride length for `x`. The `N` and `stride` parameters determine which elements in `x` are accessed at runtime. For example, to compute the [standard deviation][standard-deviation] of every other element in `x`, ```javascript var x = [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0, NaN ]; var v = nanstdevtk( 5, 1, x, 2 ); // returns 2.5 ``` Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. ```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, NaN, NaN ] ); var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element var v = nanstdevtk( 5, 1, x1, 2 ); // returns 2.5 ``` #### nanstdevtk.ndarray( N, correction, x, strideX, offsetX ) Computes the [standard deviation][standard-deviation] of a strided array ignoring `NaN` values and using a one-pass textbook algorithm and alternative indexing semantics. ```javascript var x = [ 1.0, -2.0, NaN, 2.0 ]; var v = nanstdevtk.ndarray( x.length, 1, x, 1, 0 ); // returns ~2.0817 ``` The function has the following additional parameters: - **offsetX**: 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 [standard deviation][standard-deviation] for every other element in `x` starting from the second element ```javascript var x = [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN, NaN ]; var v = nanstdevtk.ndarray( 5, 1, x, 2, 1 ); // returns 2.5 ```

## Notes - If `N <= 0`, both functions return `NaN`. - If `n - c` is less than or equal to `0` (where `c` corresponds to the provided degrees of freedom adjustment and `n` corresponds to the number of non-`NaN` indexed elements), both functions return `NaN`. - Some caution should be exercised when using the one-pass textbook algorithm. Literature overwhelmingly discourages the algorithm's use for two reasons: 1) the lack of safeguards against underflow and overflow and 2) the risk of catastrophic cancellation when subtracting the two sums if the sums are large and the variance small. These concerns have merit; however, the one-pass textbook algorithm should not be dismissed outright. For data distributions with a moderately large standard deviation to mean ratio (i.e., **coefficient of variation**), the one-pass textbook algorithm may be acceptable, especially when performance is paramount and some precision loss is acceptable (including a risk of computing a negative variance due to floating-point rounding errors!). In short, no single "best" algorithm for computing the standard deviation exists. The "best" algorithm depends on the underlying data distribution, your performance requirements, and your minimum precision requirements. When evaluating which algorithm to use, consider the relative pros and cons, and choose the algorithm which best serves your needs. - Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array-base/accessor`][@stdlib/array/base/accessor]). - Depending on the environment, the typed versions ([`dnanstdevtk`][@stdlib/stats/strided/dnanstdevtk], [`snanstdevtk`][@stdlib/stats/base/snanstdevtk], etc.) are likely to be significantly more performant.

## Examples ```javascript var uniform = require( '@stdlib/random-base-uniform' ); var filledarrayBy = require( '@stdlib/array-filled-by' ); var bernoulli = require( '@stdlib/random-base-bernoulli' ); var nanstdevtk = require( '@stdlib/stats-base-nanstdevtk' ); function rand() { if ( bernoulli( 0.8 ) < 1 ) { return NaN; } return uniform( -50.0, 50.0 ); } var x = filledarrayBy( 10, 'float64', rand ); console.log( x ); var v = nanstdevtk( x.length, 1, x, 1 ); console.log( v ); ```

## References - 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].

* * * ## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].

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license: Apache-2.0 AND BSL-1.0

date-released: 2016

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npmjs.org: @stdlib/stats-base-nanstdevtk

Calculate the standard deviation of a strided array ignoring NaN values and using a one-pass textbook algorithm.

Homepage: https://stdlib.io
License: Apache-2.0
Latest release: 0.2.2
published over 1 year ago

Versions: 14
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Downloads: 16 Last month

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@stdlib/array-float64 ^0.0.x development
@stdlib/bench ^0.0.x development
@stdlib/math-base-assert-is-nan ^0.0.x development
@stdlib/math-base-special-floor ^0.0.x development
@stdlib/math-base-special-pow ^0.0.x development
@stdlib/math-base-special-round ^0.0.x development
@stdlib/random-base-randu ^0.0.x development
istanbul ^0.4.1 development
tap-spec 5.x.x development
tape git+https://github.com/kgryte/tape.git#fix/globby development
@stdlib/math-base-special-sqrt ^0.0.x
@stdlib/stats-base-nanvariancetk ^0.0.x
@stdlib/types ^0.0.x
@stdlib/utils-define-nonenumerable-read-only-property ^0.0.x

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@stdlib/stats-base-nanstdevtk

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