@stdlib/stats-incr-kurtosis v0.2.1
incrkurtosis
Compute a corrected sample excess kurtosis incrementally.
The kurtosis for a random variable X
is defined as
Using a univariate normal distribution as the standard of comparison, the excess kurtosis is the kurtosis minus 3
.
For a sample of n
values, the sample excess kurtosis is
where m_4
is the sample fourth central moment and m_2
is the sample second central moment.
The previous equation is, however, a biased estimator of the population excess kurtosis. An alternative estimator which is unbiased under normality is
Installation
npm install @stdlib/stats-incr-kurtosis
Usage
var incrkurtosis = require( '@stdlib/stats-incr-kurtosis' );
incrkurtosis()
Returns an accumulator function
which incrementally computes a corrected sample excess kurtosis.
var accumulator = incrkurtosis();
accumulator( [x] )
If provided an input value x
, the accumulator function returns an updated corrected sample excess kurtosis. If not provided an input value x
, the accumulator function returns the current corrected sample excess kurtosis.
var accumulator = incrkurtosis();
var kurtosis = accumulator( 2.0 );
// returns null
kurtosis = accumulator( 2.0 );
// returns null
kurtosis = accumulator( -4.0 );
// returns null
kurtosis = accumulator( -4.0 );
// returns -6.0
Notes
- Input values are not type checked. If provided
NaN
or a value which, when used in computations, results inNaN
, the accumulated value isNaN
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
var randu = require( '@stdlib/random-base-randu' );
var incrkurtosis = require( '@stdlib/stats-incr-kurtosis' );
var accumulator;
var v;
var i;
// Initialize an accumulator:
accumulator = incrkurtosis();
// For each simulated datum, update the corrected sample excess kurtosis...
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.
See Also
@stdlib/stats-incr/mean
: compute an arithmetic mean incrementally.@stdlib/stats-incr/skewness
: compute a corrected sample skewness incrementally.@stdlib/stats-incr/stdev
: compute a corrected sample standard deviation incrementally.@stdlib/stats-incr/summary
: compute a statistical summary incrementally.@stdlib/stats-incr/variance
: compute an unbiased sample variance incrementally.
Notice
This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.