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Calculate the standard deviation of a single-precision floating-point strided array ignoring
NaN
values and using a two-pass algorithm.
The population standard deviation of a finite size population of size N
is given by
where the population mean is given by
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
,
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 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.
npm install @stdlib/stats-base-snanstdevpn
Alternatively,
- To load the package in a website via a
script
tag without installation and bundlers, use the ES Module available on theesm
branch (see README). - If you are using Deno, visit the
deno
branch (see README for usage intructions). - For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the
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 snanstdevpn = require( '@stdlib/stats-base-snanstdevpn' );
Computes the standard deviation of a single-precision floating-point strided array x
ignoring NaN
values and using a two-pass algorithm.
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 1.0, -2.0, NaN, 2.0 ] );
var v = snanstdevpn( 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 toN-c
wherec
corresponds to the provided degrees of freedom adjustment. When computing the standard deviation of a population, setting this parameter to0
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 to1
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
Float32Array
. - 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 Float32Array = require( '@stdlib/array-float32' );
var floor = require( '@stdlib/math-base-special-floor' );
var x = new Float32Array( [ 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 = snanstdevpn( 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 Float32Array = require( '@stdlib/array-float32' );
var floor = require( '@stdlib/math-base-special-floor' );
var x0 = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0, NaN ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length / 2 );
var v = snanstdevpn( N, 1, x1, 2 );
// returns 2.5
Computes the standard deviation of a single-precision floating-point strided array ignoring NaN
values and using a two-pass algorithm and alternative indexing semantics.
var Float32Array = require( '@stdlib/array-float32' );
var x = new Float32Array( [ 1.0, -2.0, NaN, 2.0 ] );
var v = snanstdevpn.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 Float32Array = require( '@stdlib/array-float32' );
var floor = require( '@stdlib/math-base-special-floor' );
var x = new Float32Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
var N = floor( x.length / 2 );
var v = snanstdevpn.ndarray( N, 1, x, 2, 1 );
// returns 2.5
- If
N <= 0
, both functions returnNaN
. - If
n - c
is less than or equal to0
(wherec
corresponds to the provided degrees of freedom adjustment andn
corresponds to the number of non-NaN
indexed elements), both functions returnNaN
.
var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float32Array = require( '@stdlib/array-float32' );
var snanstdevpn = require( '@stdlib/stats-base-snanstdevpn' );
var x;
var i;
x = new Float32Array( 10 );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = round( (randu()*100.0) - 50.0 );
}
console.log( x );
var v = snanstdevpn( x.length, 1, x, 1 );
console.log( v );
- 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: 496โ99. doi:10.1145/365719.365958.
- 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.
@stdlib/stats-base/dnanstdevpn
: calculate the standard deviation of a double-precision floating-point strided array ignoring NaN values and using a two-pass algorithm.@stdlib/stats-base/nanstdevpn
: calculate the standard deviation of a strided array ignoring NaN values and using a two-pass algorithm.@stdlib/stats-base/snanstdev
: calculate the standard deviation of a single-precision floating-point strided array ignoring NaN values.@stdlib/stats-base/snanvariancepn
: calculate the variance of a single-precision floating-point strided array ignoring NaN values and using a two-pass algorithm.@stdlib/stats-base/sstdevpn
: calculate the standard deviation of a single-precision floating-point strided array using a two-pass algorithm.
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