incrcv

Compute the coefficient of variation (CV) incrementally.

The corrected sample standard deviation is defined as

s equals StartRoot StartFraction 1 Over n minus 1 EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts left-parenthesis x Subscript i Baseline minus x overbar right-parenthesis squared EndRoot

and the arithmetic mean is defined as

x overbar equals StartFraction 1 Over n EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts x Subscript i

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

c Subscript v Baseline equals StartFraction s Over x overbar EndFraction

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() );