Mean
Pareto (Type I) distribution expected value.
The expected value for a Pareto (Type I) random variable is
where α > 0
is the shape parameter and β > 0
is the scale parameter.
Usage
var mean = require( '@stdlib/stats/base/dists/pareto-type1/mean' );
mean( alpha, beta )
Returns the expected value of a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
(scale parameter).
var v = mean( 2.0, 1.0 );
// returns 2.0
v = mean( 4.0, 12.0 );
// returns 16.0
v = mean( 8.0, 2.0 );
// returns ~2.286
If provided NaN
as any argument, the function returns NaN
.
var v = mean( NaN, 2.0 );
// returns NaN
v = mean( 2.0, NaN );
// returns NaN
If provided 0 < alpha <= 1
, the function returns +Infinity
.
var v = mean( 0.8, 1.0 );
// returns Infinity
If provided alpha <= 0
, the function returns NaN
.
var v = mean( 0.0, 1.0 );
// returns NaN
v = mean( -1.0, 1.0 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var v = mean( 1.0, 0.0 );
// returns NaN
v = mean( 1.0, -1.0 );
// returns NaN
Examples
var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var mean = require( '@stdlib/stats/base/dists/pareto-type1/mean' );
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 = mean( alpha, beta );
console.log( 'α: %d, β: %d, E(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}