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sstdevyc

Calculate the standard deviation of a single-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer.

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,

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

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

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

To include the bundle in a webpage,

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

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

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

sstdevyc( N, correction, x, stride )

Computes the standard deviation of a single-precision floating-point strided array x using a one-pass algorithm proposed by Youngs and Cramer.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

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

var v = sstdevyc( 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 ] );
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var N = floor( x0.length / 2 );

var v = sstdevyc( N, 1, x1, 2 );
// returns 2.5

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

Computes the standard deviation of a single-precision floating-point strided array using a one-pass algorithm proposed by Youngs and Cramer and alternative indexing semantics.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, -2.0, 2.0 ] );
var N = x.length;

var v = sstdevyc.ndarray( N, 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 = sstdevyc.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.

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-float32@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-sstdevyc@umd/browser.js"></script>
<script type="text/javascript">
(function () {

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

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

References

Youngs, Edward A., and Elliot M. Cramer. 1971. "Some Results Relevant to Choice of Sum and Sum-of-Product Algorithms." Technometrics 13 (3): 657–65. doi:10.1080/00401706.1971.10488826.

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.

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README.md

README.md

sstdevyc

Usage

sstdevyc( N, correction, x, stride )

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

Notes

Examples

References

See Also

Notice

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sstdevyc

Usage

sstdevyc( N, correction, x, stride )

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

Notes

Examples

References

See Also

Notice

Community

License

Copyright