Skip to content

nanskewness

Directory actions

More options

Directory actions

More options

Latest commit

 

History

History

nanskewness

Folders and files

NameName
Last commit message
Last commit date

parent directory

..
benchmark
benchmark
 
 
docs
docs
 
 
examples
examples
 
 
lib
lib
 
 
test
test
 
 
README.md
README.md
 
 
package.json
package.json
 
 

README.md

incrnanskewness

Compute a corrected sample skewness incrementally, ignoring NaN values.

The skewness for a random variable X is defined as

$$\mathop{\mathrm{Skewness}}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]$$

For a sample of n values, the sample skewness is

$$b_1 = \frac{m_3}{s^3} = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}$$

where m_3 is the sample third central moment and s is the sample standard deviation.

An alternative definition for the sample skewness which includes an adjustment factor (and is the implemented definition) is

$$G_1 = \frac{n^2}{(n-1)(n-2)} \frac{m_3}{s^3} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}$$

Usage

var incrnanskewness = require( '@stdlib/stats/incr/nanskewness' );

incrnanskewness()

Returns an accumulator function which incrementally computes a corrected sample skewness, ignoring NaN values.

var accumulator = incrnanskewness();

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated corrected sample skewness. If not provided an input value x, the accumulator function returns the current corrected sample skewness.

var accumulator = incrnanskewness();

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( NaN );
// returns ~0.492

skewness = accumulator();
// returns ~0.492

Notes

  • Input values are not type checked. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.

Examples

var uniform = require( '@stdlib/random/base/uniform' );
var bernoulli = require( '@stdlib/random/base/bernoulli' );
var incrnanskewness = require( '@stdlib/stats/incr/nanskewness' );

// Initialize an accumulator:
var accumulator = incrnanskewness();

// For each simulated datum, update the corrected sample skewness...
var i;
for ( i = 0; i < 100; i++ ) {
    accumulator( ( bernoulli( 0.8 ) < 1 ) ? NaN : uniform( 0.0, 100.0 ) );
}
console.log( accumulator() );