Mean

Lognormal distribution expected value.

The mean for a lognormal random variable is

double-struck upper E left-bracket upper X right-bracket equals exp left-parenthesis mu plus sigma squared slash 2 right-parenthesis

where μ is the location parameter and σ > 0 is the scale parameter. According to the definition, the natural logarithm of a random variable from a lognormal distribution follows a normal distribution.

Usage

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

mean( mu, sigma )

Returns the expected value for a lognormal distribution with location mu and scale sigma.

var y = mean( 2.0, 1.0 );
// returns ~12.182

y = mean( 0.0, 1.0 );
// returns ~1.649

y = mean( -1.0, 4.0 );
// returns ~1096.633

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

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

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

If provided sigma <= 0, the function returns NaN.

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

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

Examples

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

var sigma;
var mu;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    mu = ( randu()*10.0 ) - 5.0;
    sigma = randu() * 20.0;
    y = mean( mu, sigma );
    console.log( 'µ: %d, σ: %d, E(X;µ,σ): %d', mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}