Mean

Triangular distribution expected value.

The mean for a triangular random variable is

double-struck upper E left-bracket upper X right-bracket equals StartFraction a plus b plus c Over 3 EndFraction

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

Usage

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

mean( a, b, c )

Returns the expected value of a triangular distribution with parameters a (minimum support), b (maximum support), and c (mode).

var v = mean( 0.0, 1.0, 0.8 );
// returns ~0.6

v = mean( 4.0, 12.0, 5.0 );
// returns 7.0

v = mean( 2.0, 8.0, 5.0 );
// returns 5.0

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

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

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

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

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

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

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

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

Examples

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

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 = mean( a, b, c );
    console.log( 'a: %d, b: %d, c: %d, E(X;a,b,c): %d', a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), v.toFixed( 4 ) );
}