Calculate the variance of a double-precision floating-point strided array ignoring NaN values and using a one-pass textbook algorithm.
APACHE-2.0 License
Calculate the variance of a double-precision floating-point strided array ignoring
NaN
values and using a one-pass textbook algorithm.
The population variance of a finite size population of size N
is given by
\sigma^2 = \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 variance 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 variance, the result is biased and yields a biased sample variance. To compute an unbiased sample variance for a sample of size n
,
s^2 = \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 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.
npm install @stdlib/stats-base-dnanvariancetk
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).umd
branch (see README).The branches.md 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.
var dnanvariancetk = require( '@stdlib/stats-base-dnanvariancetk' );
Computes the variance of a double-precision floating-point strided array x
ignoring NaN
values and using a one-pass textbook algorithm.
var Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
var v = dnanvariancetk( x.length, 1, x, 1 );
// returns ~4.3333
The function has the following parameters:
0
has the effect of adjusting the divisor during the calculation of the variance according to n-c
where c
corresponds to the provided degrees of freedom adjustment and n
corresponds to the number of non-NaN
indexed elements. When computing the 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, 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).Float64Array
.x
.The N
and stride
parameters determine which elements in x
are accessed at runtime. For example, to compute the variance of every other element in x
,
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, NaN ] );
var N = floor( x.length / 2 );
var v = dnanvariancetk( N, 1, x, 2 );
// returns 6.25
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, NaN ] );
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length / 2 );
var v = dnanvariancetk( N, 1, x1, 2 );
// returns 6.25
Computes the variance of a double-precision floating-point strided array ignoring NaN
values and using a one-pass textbook algorithm and alternative indexing semantics.
var Float64Array = require( '@stdlib/array-float64' );
var x = new Float64Array( [ 1.0, -2.0, NaN, 2.0 ] );
var v = dnanvariancetk.ndarray( x.length, 1, x, 1, 0 );
// returns ~4.33333
The function has the following additional parameters:
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 variance for every other value in x
starting from the second value
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 = dnanvariancetk.ndarray( N, 1, x, 2, 1 );
// returns 6.25
N <= 0
, both functions return NaN
.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
.var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float64Array = require( '@stdlib/array-float64' );
var dnanvariancetk = require( '@stdlib/stats-base-dnanvariancetk' );
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 = dnanvariancetk( x.length, 1, x, 1 );
console.log( v );
@stdlib/stats-base/dvariancetk
: calculate the variance of a double-precision floating-point strided array using a one-pass textbook algorithm.
@stdlib/stats-base/dnanvariance
: calculate the variance of a double-precision floating-point strided array ignoring NaN values.
@stdlib/stats-base/nanvariancetk
: calculate the variance of a strided array ignoring NaN values and using a one-pass textbook algorithm.
@stdlib/stats-base/snanvariancetk
: calculate the variance of a single-precision floating-point strided array ignoring NaN values and using a one-pass textbook algorithm.
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.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.