Standard Deviation

Pareto (Type I) distribution standard deviation.

The standard deviation for a Pareto (Type I) random variable is

where α > 0 is the shape parameter and β > 0 is the scale parameter.

Installation

npm install @stdlib/stats-base-dists-pareto-type1-stdev

Usage

var stdev = require( '@stdlib/stats-base-dists-pareto-type1-stdev' );

stdev( alpha, beta )

Returns the standard deviation of a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

var v = stdev( 2.5, 1.0 );
// returns ~1.491

v = stdev( 4.0, 12.0 );
// returns ~5.657

v = stdev( 8.0, 2.0 );
// returns ~0.33

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

var v = stdev( NaN, 2.0 );
// returns NaN

v = stdev( 2.0, NaN );
// returns NaN

If provided 0 < alpha <= 2, the function returns +Infinity.

var v = stdev( 0.5, 2.0 );
// returns Infinity

v = stdev( 1.5, 1.0 );
// returns Infinity

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

var v = stdev( 0.0, 1.0 );
// returns NaN

v = stdev( -1.0, 1.0 );
// returns NaN

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

var v = stdev( 1.0, 0.0 );
// returns NaN

v = stdev( 1.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var stdev = require( '@stdlib/stats-base-dists-pareto-type1-stdev' );

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + EPS;
    v = stdev( alpha, beta );
    console.log( 'α: %d, β: %d, Var(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}

Notice

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.