stdlib-js
<summary>
About stdlib...
</summary>
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!
variancepn
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
Calculate the [variance][variance] of a strided array using a two-pass algorithm.
N is given by
n,
where the sample mean is given by
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 variance and population variance. Depending on the characteristics of the population distribution, other correction factors (e.g., n-1.5, n+1, etc) can yield better estimators.
bash
npm install @stdlib/stats-base-variancepn
javascript
var variancepn = require( '@stdlib/stats-base-variancepn' );
#### variancepn( N, correction, x, stride )
Computes the [variance][variance] of a strided array x using a two-pass algorithm.
javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;
var v = variancepn( N, 1, x, 1 );
// returns ~4.3333
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 [variance][variance] according to N-c where c corresponds to the provided degrees of freedom adjustment. When computing the [variance][variance] 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 unbiased sample [variance][variance], 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].
- stride: index increment for x.
The N and stride parameters determine which elements in x are accessed at runtime. For example, to compute the [variance][variance] 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 ];
var N = floor( x.length / 2 );
var v = variancepn( N, 1, x, 2 );
// returns 6.25
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 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 = variancepn( N, 1, x1, 2 );
// returns 6.25
#### variancepn.ndarray( N, correction, x, stride, offset )
Computes the [variance][variance] of a strided array using a two-pass algorithm and alternative indexing semantics.
javascript
var x = [ 1.0, -2.0, 2.0 ];
var N = x.length;
var v = variancepn.ndarray( N, 1, x, 1, 0 );
// returns ~4.33333
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 [variance][variance] 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 ];
var N = floor( x.length / 2 );
var v = variancepn.ndarray( N, 1, x, 2, 1 );
// returns 6.25
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 ([dvariancepn][@stdlib/stats/base/dvariancepn], [svariancepn][@stdlib/stats/base/svariancepn], etc.) are likely to be significantly more performant.
javascript
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float64Array = require( '@stdlib/array-float64' );
var variancepn = require( '@stdlib/stats-base-variancepn' );
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 = variancepn( x.length, 1, x, 1 );
console.log( v );
@stdlib/stats-base/dvariancepn][@stdlib/stats/base/dvariancepn]: calculate the variance of a double-precision floating-point strided array using a two-pass algorithm.
- [@stdlib/stats-base/nanvariancepn][@stdlib/stats/base/nanvariancepn]: calculate the variance of a strided array ignoring NaN values and using a two-pass algorithm.
- [@stdlib/stats-base/stdevpn][@stdlib/stats/base/stdevpn]: calculate the standard deviation of a strided array using a two-pass algorithm.
- [@stdlib/stats-base/variance][@stdlib/stats/base/variance]: calculate the variance of a strided array.
