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Evaluate the natural logarithm of the probability density function (PDF) for a Pareto (Type I) distribution.
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.
import logpdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-logpdf@esm/index.mjs';
You can also import the following named exports from the package:
import { factory } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-logpdf@esm/index.mjs';
Evaluates the natural logarithm of the probability density function (PDF) for a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
(scale parameter).
var y = logpdf( 4.0, 1.0, 1.0 );
// returns ~-2.773
y = logpdf( 20.0, 1.0, 10.0 );
// returns ~-3.689
y = logpdf( 7.0, 2.0, 6.0 );
// returns ~-1.561
y = logpdf( 7.0, 6.0, 3.0 );
// returns ~-5.238
y = logpdf( 1.0, 4.0, 2.0 );
// returns -Infinity
y = logpdf( 1.5, 4.0, 2.0 );
// returns -Infinity
If provided NaN
as any argument, the function returns NaN
.
var y = logpdf( NaN, 1.0, 1.0 );
// returns NaN
y = logpdf( 0.0, NaN, 1.0 );
// returns NaN
y = logpdf( 0.0, 1.0, NaN );
// returns NaN
If provided alpha <= 0
, the function returns NaN
.
var y = logpdf( 2.0, -1.0, 0.5 );
// returns NaN
y = logpdf( 2.0, 0.0, 0.5 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var y = logpdf( 2.0, 0.5, -1.0 );
// returns NaN
y = logpdf( 2.0, 0.5, 0.0 );
// returns NaN
Returns a function for evaluating the natural logarithm of the probability density function (PDF) (CDF) of a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
(scale parameter).
var mylogpdf = logpdf.factory( 0.5, 0.5 );
var y = mylogpdf( 0.8 );
// returns ~-0.705
y = mylogpdf( 2.0 );
// returns ~-2.079
- In virtually all cases, using the
logpdf
orlogcdf
functions is preferable to manually computing the logarithm of thepdf
orcdf
, respectively, since the latter is prone to overflow and underflow.
<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">
import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import logpdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-pareto-type1-logpdf@esm/index.mjs';
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 = logpdf( x, alpha, beta );
console.log( 'x: %d, α: %d, β: %d, ln(f(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}
</script>
</body>
</html>
This package is part of stdlib, a standard library 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.
See LICENSE.
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