# 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/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 ) );
}