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incrcv

Compute the coefficient of variation (CV) incrementally.

The corrected sample standard deviation is defined as

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

and the arithmetic mean is defined as

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

The coefficient of variation (also known as relative standard deviation, RSD) is defined as

$$c_v = \frac{s}{\bar{x}}$$

Installation

npm install @stdlib/stats-incr-cv

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm 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.

Usage

var incrcv = require( '@stdlib/stats-incr-cv' );

incrcv( [mean] )

Returns an accumulator function which incrementally computes the coefficient of variation.

var accumulator = incrcv();

If the mean is already known, provide a mean argument.

var accumulator = incrcv( 3.0 );

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated accumulated value. If not provided an input value x, the accumulator function returns the current accumulated value.

var accumulator = incrcv();

var cv = accumulator( 2.0 );
// returns 0.0

cv = accumulator( 1.0 ); // => s^2 = ((2-1.5)^2+(1-1.5)^2) / (2-1)
// returns ~0.47

cv = accumulator( 3.0 ); // => s^2 = ((2-2)^2+(1-2)^2+(3-2)^2) / (3-1)
// returns 0.5

cv = accumulator();
// returns 0.5

Notes

• Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for all future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
• The coefficient of variation is typically computed on nonnegative values. The measure may lack meaning for data which can assume both positive and negative values.
• For small and moderately sized samples, the accumulated value tends to be too low and is thus a biased estimator. Provided the generating distribution is known (e.g., a normal distribution), you may want to adjust the accumulated value or use an alternative implementation providing an unbiased estimator.

Examples

var randu = require( '@stdlib/random-base-randu' );
var incrcv = require( '@stdlib/stats-incr-cv' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrcv();

// For each simulated datum, update the coefficient of variation...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );

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See Also

• @stdlib/stats-incr/mean: compute an arithmetic mean incrementally.
• @stdlib/stats-incr/mcv: compute a moving coefficient of variation (CV) incrementally.
• @stdlib/stats-incr/stdev: compute a corrected sample standard deviation incrementally.
• @stdlib/stats-incr/vmr: compute a variance-to-mean ratio (VMR) incrementally.

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.