Skewness

Binomial distribution skewness.

The skewness for a binomial random variable is

s k e w left-parenthesis upper X right-parenthesis equals StartFraction 1 minus 2 p Over StartRoot n p left-parenthesis 1 minus p right-parenthesis EndRoot EndFraction

where n is the number of trials and p is the success probability.

Usage

var skewness = require( '@stdlib/math/base/dists/binomial/skewness' );

skewness( n, p )

Returns the skewness of a binomial distribution with number of trials n and success probability p.

var v = skewness( 20, 0.1 );
// returns ~0.596

v = skewness( 50, 0.5 );
// returns 0

If provided NaN as any argument, the function returns NaN.

var v = skewness( NaN, 0.5 );
// returns NaN

v = skewness( 20, NaN );
// returns NaN

If provided a number of trials n which is not a nonnegative integer, the function returns NaN.

var v = skewness( 1.5, 0.5 );
// returns NaN

v = skewness( -2.0, 0.5 );
// returns NaN

If provided a success probability p outside of [0,1], the function returns NaN.

var v = skewness( 20, -1.0 );
// returns NaN

v = skewness( 20, 1.5 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var skewness = require( '@stdlib/math/base/dists/binomial/skewness' );

var v;
var i;
var n;
var p;

for ( i = 0; i < 10; i++ ) {
    n = round( randu() * 100.0 );
    p = randu();
    v = skewness( n, p );
    console.log( 'n: %d, p: %d, skew(X;n,p): %d', n, p.toFixed( 4 ), v.toFixed( 4 ) );
}