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Lognormal distribution differential entropy.

The differential entropy (in nats) for a lognormal random variable is

Differential entropy for a lognormal distribution.

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.


npm install @stdlib/stats-base-dists-lognormal-entropy


var entropy = require( '@stdlib/stats-base-dists-lognormal-entropy' );

entropy( mu, sigma )

Returns the differential entropy for a lognormal distribution with location mu and scale sigma (in nats).

var y = entropy( 2.0, 1.0 );
// returns ~3.419

y = entropy( 0.0, 1.0 );
// returns ~1.419

y = entropy( -1.0, 2.0 );
// returns ~1.112

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

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

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

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

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

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


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

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


This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.






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