Variance

Lognormal distribution variance.

The variance for a lognormal random variable is

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 variance = require( '@stdlib/stats/base/dists/lognormal/variance' );

variance( mu, sigma )

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

var y = variance( 2.0, 1.0 );
// returns ~255.016

y = variance( 0.0, 1.0 );
// returns ~4.671

y = variance( -1.0, 2.0 );
// returns ~396.04

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

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

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

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

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

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var variance = require( '@stdlib/stats/base/dists/lognormal/variance' );

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 = variance( mu, sigma );
    console.log( 'µ: %d, σ: %d, Var(X;µ,σ): %d', mu.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

#include "stdlib/stats/base/dists/lognormal/variance.h"

stdlib_base_dists_lognormal_variance( mu, sigma )

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

double out = stdlib_base_dists_lognormal_variance( 0.0, 1.0 );
// returns ~4.671

The function accepts the following arguments:

mu: [in] double location parameter.
sigma: [in] double scale parameter.

double stdlib_base_dists_lognormal_variance( const double mu, const double sigma );

Examples

#include "stdlib/stats/base/dists/lognormal/variance.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double sigma;
    double mu;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        mu = random_uniform( -5.0, 5.0 );
        sigma = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_lognormal_variance( mu, sigma );
        printf( "µ: %lf, σ: %lf, Var(X;µ,σ): %lf\n", mu, sigma, y );
    }
}