Logarithm of Probability Density Function

Evaluate the natural logarithm of the probability density function for a Kumaraswamy's double bounded distribution.

The probability density function (PDF) for a Kumaraswamy's double bounded random variable is

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where a > 0 is the first shape parameter and b > 0 is the second shape parameter.

Usage

var logpdf = require( '@stdlib/stats/base/dists/kumaraswamy/logpdf' );

logpdf( x, a, b )

Evaluates the natural logarithm of the probability density function (PDF) for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

var y = logpdf( 0.5, 1.0, 1.0 );
// returns 0.0

y = logpdf( 0.5, 2.0, 4.0 );
// returns ~0.523

y = logpdf( 0.2, 2.0, 2.0 );
// returns ~-0.264

y = logpdf( 0.8, 4.0, 4.0 );
// returns ~0.522

y = logpdf( -0.5, 4.0, 2.0 );
// returns -Infinity

y = logpdf( -Infinity, 4.0, 2.0 );
// returns -Infinity

y = logpdf( 1.5, 4.0, 2.0 );
// returns -Infinity

y = logpdf( +Infinity, 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 a <= 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 b <= 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

logpdf.factory( a, b )

Returns a function for evaluating the natural logarithm of the probability density function (PDF) for a Kumaraswamy's double bounded distribution with parameters a (first shape parameter) and b (second shape parameter).

var mylogpdf = logpdf.factory( 0.5, 0.5 );

var y = mylogpdf( 0.8 );
// returns ~-0.151

y = mylogpdf( 0.3 );
// returns ~-0.388

Notes

  • In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var logpdf = require( '@stdlib/stats/base/dists/kumaraswamy/logpdf' );

var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu();
    a = ( randu()*5.0 ) + EPS;
    b = ( randu()*5.0 ) + EPS;
    y = logpdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, ln(f(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}