Probability Density Function
Pareto (Type I) distribution probability density function (PDF).
The probability density function (PDF) for a Pareto (Type I) random variable is
where alpha > 0
is the shape parameter and beta > 0
is the scale parameter.
Usage
var pdf = require( '@stdlib/stats/base/dists/pareto-type1/pdf' );
pdf( x, alpha, beta )
Evaluates the probability density function (PDF) for a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
(scale parameter).
var y = pdf( 4.0, 1.0, 1.0 );
// returns ~0.063
y = pdf( 20.0, 1.0, 10.0 );
// returns 0.025
y = pdf( 7.0, 2.0, 6.0 );
// returns ~0.21
y = pdf( 7.0, 6.0, 3.0 );
// returns ~0.005
y = pdf( 1.0, 4.0, 2.0 );
// returns 0.0
y = pdf( 1.5, 4.0, 2.0 );
// returns 0.0
If provided NaN
as any argument, the function returns NaN
.
var y = pdf( NaN, 1.0, 1.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0 );
// returns NaN
y = pdf( 0.0, 1.0, NaN );
// returns NaN
If provided alpha <= 0
, the function returns NaN
.
var y = pdf( 2.0, -1.0, 0.5 );
// returns NaN
y = pdf( 2.0, 0.0, 0.5 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var y = pdf( 2.0, 0.5, -1.0 );
// returns NaN
y = pdf( 2.0, 0.5, 0.0 );
// returns NaN
pdf.factory( alpha, beta )
Returns a function for evaluating the probability density function (PDF) (CDF) of a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
(scale parameter).
var mypdf = pdf.factory( 0.5, 0.5 );
var y = mypdf( 0.8 );
// returns ~0.494
y = mypdf( 2.0 );
// returns ~0.125
Examples
var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/stats/base/dists/pareto-type1/pdf' );
var alpha;
var beta;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu() * 8.0;
alpha = randu() * 4.0;
beta = randu() * 4.0;
y = pdf( x, alpha, beta );
console.log( 'x: %d, α: %d, β: %d, f(x;α,β): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}