# incrmcv
> Compute a moving [coefficient of variation][coefficient-of-variation] (CV) incrementally.
For a window of size `W`, the [corrected sample standard deviation][standard-deviation] is defined as
and the [arithmetic mean][arithmetic-mean] is defined as
The [coefficient of variation][coefficient-of-variation] (also known as **relative standard deviation**, RSD) is defined as
## Usage
```javascript
var incrmcv = require( '@stdlib/stats/incr/mcv' );
```
#### incrmcv( window\[, mean] )
Returns an accumulator `function` which incrementally computes a moving [coefficient of variation][coefficient-of-variation]. The `window` parameter defines the number of values over which to compute the moving [coefficient of variation][coefficient-of-variation].
```javascript
var accumulator = incrmcv( 3 );
```
If the mean is already known, provide a `mean` argument.
```javascript
var accumulator = incrmcv( 3, 5.0 );
```
#### 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.
```javascript
var accumulator = incrmcv( 3 );
var cv = accumulator();
// returns null
// Fill the window...
cv = accumulator( 2.0 ); // [2.0]
// returns 0.0
cv = accumulator( 1.0 ); // [2.0, 1.0]
// returns ~0.47
cv = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns 0.5
// Window begins sliding...
cv = accumulator( 7.0 ); // [1.0, 3.0, 7.0]
// returns ~0.83
cv = accumulator( 5.0 ); // [3.0, 7.0, 5.0]
// returns ~0.40
cv = accumulator();
// returns ~0.40
```
## 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 **at least** `W-1` 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.
- As `W` values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
- The [coefficient of variation][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
```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrmcv = require( '@stdlib/stats/incr/mcv' );
var accumulator;
var v;
var i;
// Initialize an accumulator:
accumulator = incrmcv( 5 );
// For each simulated datum, update the moving coefficient of variation...
for ( i = 0; i < 100; i++ ) {
v = randu() * 100.0;
accumulator( v );
}
console.log( accumulator() );
```
[coefficient-of-variation]: https://en.wikipedia.org/wiki/Coefficient_of_variation
[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean
[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation
