Compute a corrected sample excess kurtosis incrementally.
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Compute a [corrected sample excess kurtosis][sample-excess-kurtosis] incrementally.
X is defined asmath
\mathop{\mathrm{Kurtosis}}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^4 \biggr]3.n values, the [sample excess kurtosis][sample-excess-kurtosis] ismath
g_2 = \frac{m_4}{m_2^2} - 3 = \frac{\frac{1}{n} \displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\frac{1}{n} \displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2}m_4 is the sample fourth central moment and m_2 is the sample second central moment.math
G_2 = \frac{(n+1)n}{(n-1)(n-2)(n-3)} \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2} - 3 \frac{(n-1)^2}{(n-2)(n-3)}bash
npm install @stdlib/stats-incr-kurtosisscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var incrkurtosis = require( '@stdlib/stats-incr-kurtosis' );function which incrementally computes a [corrected sample excess kurtosis][sample-excess-kurtosis].javascript
var accumulator = incrkurtosis();x, the accumulator function returns an updated [corrected sample excess kurtosis][sample-excess-kurtosis]. If not provided an input value x, the accumulator function returns the current [corrected sample excess kurtosis][sample-excess-kurtosis].javascript
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 -6.0NaN 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.javascript
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() );
