Triangular distribution logarithm of probability density function (PDF).
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[Triangular][triangular-distribution] distribution logarithm of [probability density function][pdf] (PDF).
math
f(x;a,b,c)=\begin{cases} 0 & \text{for } x < a \\ \frac{2(x-a)}{(b-a)(c-a)} & \text{for } a \le x < c \\ \frac{2}{b-a} & \text{for } x = c \\ \frac{2(b-x)}{(b-a)(b-c)} & \text{for } c < x \le b \\ 0 & \text{for } b < x \end{cases}a is the lower limit and b is the upper limit and c is the mode.bash
npm install @stdlib/stats-base-dists-triangular-logpdfscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var logpdf = require( '@stdlib/stats-base-dists-triangular-logpdf' );a (lower limit), b (upper limit) and c (mode).javascript
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 -InfinityNaN as any argument, the function returns NaN.javascript
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 NaNa <= c <= b, the function returns NaN.javascript
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 NaNa (lower limit), b (upper limit), and c (mode).javascript
var mylogpdf = logpdf.factory( 0.0, 10.0, 5.0 );
var y = mylogpdf( 2.0 );
// returns ~-2.526
y = mylogpdf( 12.0 );
// returns -Infinitylogpdf 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.javascript
var uniform = require( '@stdlib/random-base-uniform' );
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 = uniform( 0.0, 30.0 );
a = uniform( 0.0, 10.0 );
b = uniform( a, a + 40.0 );
c = uniform( a, b );
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 ) );
}c
#include "stdlib/stats/base/dists/triangular/logpdf.h"a (lower limit), b (upper limit), and c (mode).c
double y = stdlib_base_dists_triangular_logpdf( 0.5, -1.0, 1.0, 0.0 );
// returns ~-0.693[in] double input value.[in] double lower limit.[in] double upper limit.[in] double mode.c
double stdlib_base_dists_triangular_logpdf( const double x, const double a, const double b, const double c );c
#include "stdlib/stats/base/dists/triangular/logpdf.h"
#include "stdlib/constants/float64/eps.h"
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
static double random_uniform( const double min, const double max ) {
double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
return min + ( v*(max-min) );
}
int main( void ) {
double a;
double b;
double c;
double x;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
x = random_uniform( 0.0, 30.0 );
a = random_uniform( 0.0, 10.0 );
b = random_uniform( a + STDLIB_CONSTANT_FLOAT64_EPS, 40.0 );
c = random_uniform( a, b );
y = stdlib_base_dists_triangular_logpdf( x, a, b, c );
printf( "x: %lf, a: %lf, b: %lf, c: %lf, ln(f(x;a,b,c)): %lf\n", x, a, b, c, y );
}
}
