Kurtosis
Binomial distribution excess kurtosis.
The excess kurtosis for a binomial random variable is
where n
is the number of trials and p
is the success probability.
Usage
var kurtosis = require( '@stdlib/stats/base/dists/binomial/kurtosis' );
kurtosis( n, p )
Returns the excess kurtosis of a binomial distribution with number of trials n
and success probability p
.
var v = kurtosis( 20, 0.1 );
// returns ~0.256
v = kurtosis( 50, 0.5 );
// returns ~-0.04
If provided NaN
as any argument, the function returns NaN
.
var v = kurtosis( NaN, 0.5 );
// returns NaN
v = kurtosis( 20, NaN );
// returns NaN
If provided a number of trials n
which is not a nonnegative integer, the function returns NaN
.
var v = kurtosis( 1.5, 0.5 );
// returns NaN
v = kurtosis( -2.0, 0.5 );
// returns NaN
If provided a success probability p
outside of [0,1]
, the function returns NaN
.
var v = kurtosis( 20, -1.0 );
// returns NaN
v = kurtosis( 20, 1.5 );
// returns NaN
Examples
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var kurtosis = require( '@stdlib/stats/base/dists/binomial/kurtosis' );
var v;
var i;
var n;
var p;
for ( i = 0; i < 10; i++ ) {
n = round( randu() * 100.0 );
p = randu();
v = kurtosis( n, p );
console.log( 'n: %d, p: %d, Kurt(X;n,p): %d', n, p.toFixed( 4 ), v.toFixed( 4 ) );
}