time-to-botec/squiggle/node_modules/@stdlib/stats/incr/mcv/README.md

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# incrmcv

> Compute a moving [coefficient of variation][coefficient-of-variation] (CV) incrementally.

<section class="intro">

For a window of size `W`, the [corrected sample standard deviation][standard-deviation] is defined as

<!-- <equation class="equation" label="eq:corrected_sample_standard_deviation" align="center" raw="s = \sqrt{\frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2}" alt="Equation for the corrected sample standard deviation."> -->

<div class="equation" align="center" data-raw-text="s = \sqrt{\frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2}" data-equation="eq:corrected_sample_standard_deviation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@eed6b690d7c37249b04544b3f5fd36ad8eb3187f/lib/node_modules/@stdlib/stats/incr/mcv/docs/img/equation_corrected_sample_standard_deviation.svg" alt="Equation for the corrected sample standard deviation.">
    <br>
</div>

<!-- </equation> -->

and the [arithmetic mean][arithmetic-mean] is defined as

<!-- <equation class="equation" label="eq:arithmetic_mean" align="center" raw="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" alt="Equation for the arithmetic mean."> -->

<div class="equation" align="center" data-raw-text="\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i" data-equation="eq:arithmetic_mean">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@4cf17e4e25cc2244d5154bd5d251f4bd023748da/lib/node_modules/@stdlib/stats/incr/mcv/docs/img/equation_arithmetic_mean.svg" alt="Equation for the arithmetic mean.">
    <br>
</div>

<!-- </equation> -->

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

<!-- <equation class="equation" label="eq:coefficient_of_variation" align="center" raw="c_v = \frac{s}{\bar{x}}" alt="Equation for the coefficient of variation (CV)."> -->

<div class="equation" align="center" data-raw-text="c_v = \frac{s}{\bar{x}}" data-equation="eq:coefficient_of_variation">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@eed6b690d7c37249b04544b3f5fd36ad8eb3187f/lib/node_modules/@stdlib/stats/incr/mcv/docs/img/equation_coefficient_of_variation.svg"Equation for the coefficient of variation (CV).">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## 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
```

</section>

<!-- /.usage -->

<section class="notes">

## 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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```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() );
```

</section>

<!-- /.examples -->

<section class="links">

[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

</section>

<!-- /.links -->