Skewness

Triangular distribution skewness.

The skewness for a triangular random variable is

s k e w left-parenthesis upper X right-parenthesis equals StartFraction StartRoot 2 EndRoot left-parenthesis a plus b minus 2 c right-parenthesis left-parenthesis 2 a minus b minus c right-parenthesis left-parenthesis a minus 2 b plus c right-parenthesis Over 5 left-parenthesis a squared plus b squared plus c squared minus a b minus a c minus b c right-parenthesis Superscript three-halves Baseline EndFraction

where a is the lower limit, b is the upper limit and c is the mode.

Usage

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

skewness( a, b, c )

Returns the skewness of a triangular distribution with minimum support a, maximum supportb, and mode c.

var v = skewness( 0.0, 1.0, 0.8 );
// returns ~-0.476

v = skewness( 4.0, 12.0, 5.0 );
// returns ~0.532

v = skewness( 2.0, 8.0, 5.0 );
// returns 0.0

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

var v = skewness( NaN, 4.0, 2.0 );
// returns NaN

v = skewness( 0.0, NaN, 2.0 );
// returns NaN

v = skewness( 0.0, 4.0, NaN );
// returns NaN

If provided parameters not satisfying a <= c <= b, the function returns NaN.

var y = skewness( 1.0, 0.0, 1.5 );
// returns NaN

y = skewness( 0.0, 1.0, -1.0 );
// returns NaN

y = skewness( 0.0, -1.0, 0.5 );
// returns NaN

Examples

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

var a;
var b;
var c;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = ( randu()*10.0 );
    b = ( randu()*10.0 ) + a;
    c = ( randu()*( b-a ) ) + a;
    v = skewness( a, b, c );
    console.log( 'a: %d, b: %d, c: %d, skew(X;a,b,c): %d', a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), v.toFixed( 4 ) );
}