Logarithm of Cumulative Distribution Function

Triangular distribution logarithm of cumulative distribution function.

The cumulative distribution function for a triangular random variable is

upper F left-parenthesis x semicolon a comma b comma c right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 0 2nd Column for x less-than-or-equal-to a 2nd Row 1st Column StartFraction left-parenthesis x minus a right-parenthesis squared Over left-parenthesis b minus a right-parenthesis left-parenthesis c minus a right-parenthesis EndFraction 2nd Column for a less-than x less-than-or-equal-to c 3rd Row 1st Column 1 minus StartFraction left-parenthesis b minus x right-parenthesis squared Over left-parenthesis b minus a right-parenthesis left-parenthesis b minus c right-parenthesis EndFraction 2nd Column for c less-than x less-than b 4th Row 1st Column 1 2nd Column for b less-than-or-equal-to x EndLayout

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

Usage

var logcdf = require( '@stdlib/math/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

Examples

var randu = require( '@stdlib/random/base/randu' );
var logcdf = require( '@stdlib/math/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 ) );
}