Logarithm of Cumulative Distribution Function

Triangular distribution logarithm of cumulative distribution function.

The cumulative distribution function for a triangular random variable is

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

Usage

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

logcdf( x, a, b, c )

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

var y = logcdf( 0.5, -1.0, 1.0, 0.0 );
// returns ~-0.134

y = logcdf( 0.5, -1.0, 1.0, 0.5 );
// returns ~-0.288

y = logcdf( -10.0, -20.0, 0.0, -2.0 );
// returns ~-1.281

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

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

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

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

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

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

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

var y = logcdf( 2.0, 1.0, 0.0, 1.5 );
// returns NaN

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

y = logcdf( 2.0, 0.0, -1.0, 0.5 );
// returns NaN

logcdf.factory( a, b, c )

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

var mylogcdf = logcdf.factory( 0.0, 10.0, 2.0 );
var y = mylogcdf( 0.5 );
// returns ~-4.382

y = mylogcdf( 8.0 );
// returns ~-0.051

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

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 = logcdf( 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 ) );
}