# incrskewness
> Compute a [corrected sample skewness][sample-skewness] incrementally.
The [skewness][sample-skewness] for a random variable `X` is defined as
For a sample of `n` values, the [sample skewness][sample-skewness] is
where `m_3` is the sample third central moment and `s` is the sample standard deviation.
An alternative definition for the [sample skewness][sample-skewness] which includes an adjustment factor (and is the implemented definition) is
## Usage
```javascript
var incrskewness = require( '@stdlib/stats/incr/skewness' );
```
#### incrskewness()
Returns an accumulator `function` which incrementally computes a [corrected sample skewness][sample-skewness].
```javascript
var accumulator = incrskewness();
```
#### accumulator( \[x] )
If provided an input value `x`, the accumulator function returns an updated [corrected sample skewness][sample-skewness]. If not provided an input value `x`, the accumulator function returns the current [corrected sample skewness][sample-skewness].
```javascript
var accumulator = incrskewness();
var skewness = accumulator();
// returns null
skewness = accumulator( 2.0 );
// returns null
skewness = accumulator( -5.0 );
// returns null
skewness = accumulator( -10.0 );
// returns ~0.492
skewness = accumulator();
// returns ~0.492
```
## 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.
## Examples
```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrskewness = require( '@stdlib/stats/incr/skewness' );
var accumulator;
var v;
var i;
// Initialize an accumulator:
accumulator = incrskewness();
// For each simulated datum, update the corrected sample skewness...
for ( i = 0; i < 100; i++ ) {
v = randu() * 100.0;
accumulator( v );
}
console.log( accumulator() );
```
* * *
## References
- Joanes, D. N., and C. A. Gill. 1998. "Comparing measures of sample skewness and kurtosis." _Journal of the Royal Statistical Society: Series D (The Statistician)_ 47 (1). Blackwell Publishers Ltd: 183–89. doi:[10.1111/1467-9884.00122][@joanes:1998].
[sample-skewness]: https://en.wikipedia.org/wiki/Skewness
[@joanes:1998]: http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00122/
