Logarithm of Probability Density Function

Triangular distribution logarithm of probability density function (PDF).

The probability density function (PDF) for a triangular random variable is

where a is the lower limit and b is the upper limit and c is the mode.

Usage

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

logpdf( x, a, b, c )

Evaluates the natural logarithm of the probability density function (PDF) for a triangular distribution with parameters a (lower limit), b (upper limit) and c (mode).

var y = logpdf( 0.5, -1.0, 1.0, 0.0 );
// returns ~-0.693

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

y = logpdf( -10.0, -20.0, 0.0, -2.0 );
// returns ~-2.89

y = logpdf( -2.0, -1.0, 1.0, 0.0 );
// returns -Infinity

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

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

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

y = logpdf( 0.0, 0.0, NaN, 0.5 );
// returns NaN

y = logpdf( 2.0, 1.0, 0.0, NaN );
// returns NaN

If provided parameters not satisfying a <= c <= b, the function returns NaN.

var y = logpdf( 1.0, 1.0, 0.0, 1.5 );
// returns NaN

y = logpdf( 1.0, 1.0, 0.0, -1.0 );
// returns NaN

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

logpdf.factory( a, b, c )

Returns a function for evaluating the natural logarithm of the probability density function (PDF) of a triangular distribution with parameters a (lower limit), b (upper limit) and c (mode).

var mylogpdf = logpdf.factory( 0.0, 10.0, 5.0 );
var y = mylogpdf( 2.0 );
// returns ~-2.526

y = mylogpdf( 12.0 );
// returns -Infinity

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

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

for ( i = 0; i < 25; i++ ) {
    x = randu() * 30.0;
    a = randu() * 10.0;
    b = a + (randu() * 40.0);
    c = a + ((b-a) * randu());
    y = logpdf( x, a, b, c );
    console.log( 'x: %d, a: %d, b: %d, c: %d, ln(f(x;a,b,c)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), y.toFixed( 4 ) );
}