Skip to content

Latest commit

 

History

History
384 lines (242 loc) · 15.2 KB

README.md

File metadata and controls

384 lines (242 loc) · 15.2 KB
Raw
About stdlib...

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.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

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!

stdev

NPM version Build Status Coverage Status

Calculate the standard deviation of a strided array.

The population standard deviation of a finite size population of size N is given by

$$\sigma = \sqrt{\frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu)^2}$$

where the population mean is given by

$$\mu = \frac{1}{N} \sum_{i=0}^{N-1} x_i$$

Often in the analysis of data, the true population 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, the result is biased and yields an uncorrected sample standard deviation. To compute a corrected sample standard deviation for a sample of size n,

$$s = \sqrt{\frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2}$$

where the sample mean is given by

$$\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i$$

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.

Usage

To use in Observable,

stdev = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-stdev@umd/browser.js' )

To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:

var stdev = require( 'path/to/vendor/umd/stats-base-stdev/index.js' )

To include the bundle in a webpage,

<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-stdev@umd/browser.js"></script>

If no recognized module system is present, access bundle contents via the global scope:

<script type="text/javascript">
(function () {
    window.stdev;
})();
</script>

stdev( N, correction, x, stride )

Computes the standard deviation of a strided array x.

var x = [ 1.0, -2.0, 2.0 ];

var v = stdev( 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 according to N-c where c corresponds to the provided degrees of freedom adjustment. When computing the 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, 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 or 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 standard deviation of every other element in x,

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 ];
var N = floor( x.length / 2 );

var v = stdev( N, 1, x, 2 );
// returns 2.5

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

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 = stdev( N, 1, x1, 2 );
// returns 2.5

stdev.ndarray( N, correction, x, stride, offset )

Computes the standard deviation of a strided array using alternative indexing semantics.

var x = [ 1.0, -2.0, 2.0 ];

var v = stdev.ndarray( x.length, 1, x, 1, 0 );
// returns ~2.0817

The function has the following additional parameters:

  • offset: starting index for x.

While 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 for every other value in x starting from the second value

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 ];
var N = floor( x.length / 2 );

var v = stdev.ndarray( N, 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), both functions return NaN.
  • Depending on the environment, the typed versions (dstdev, sstdev, etc.) are likely to be significantly more performant.

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-round@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-stdev@umd/browser.js"></script>
<script type="text/javascript">
(function () {

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 = stdev( x.length, 1, x, 1 );
console.log( v );

})();
</script>
</body>
</html>

See Also

Notice

This package is part of 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, see the main project repository.

Community

Chat

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.