@stdlib/stats-base-dists-triangular-logcdf
v0.3.1TypeScript
Triangular distribution logarithm of cumulative distribution function (CDF).
stdlibstdmathstatisticsstatsdistributiondistprobabilitycdfcumulative distributiondistribution function
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Published by The Stdlib Authors
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About stdlib...
Logarithm of Cumulative Distribution Function
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> [Triangular][triangular-distribution] distribution logarithm of [cumulative distribution function][cdf].
The [cumulative distribution function][cdf] for a [triangular][triangular-distribution] random variable is
where a is the lower limit, b is the upper limit, and c is the mode.
Installation
``bash`
npm install @stdlib/stats-base-dists-triangular-logcdf
Usage
`javascript`
var logcdf = require( '@stdlib/stats-base-dists-triangular-logcdf' );
#### logcdf( x, a, b, c )
Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [triangular][triangular-distribution] distribution with parameters a (lower limit), b (upper limit) and c (mode).
`javascript
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.
`javascript
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.
`javascript
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][cdf] of a [triangular][triangular-distribution] distribution with parameters a (lower limit), b (upper limit) and c (mode).
`javascript
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
`javascript
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 ) );
}
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/geometric/logcdf.h"
#### stdlib_base_dists_geometric_logcdf( x, a, b, c )
Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [triangular][triangular-distribution] distribution with parameters a (lower limit), b (upper limit), and c (mode).
`c`
double y = stdlib_base_dists_geometric_logcdf( 0.5, -1.0, 1.0, 0.0 );
// returns ~-0.134
The function accepts the following arguments:
- x: [in] double input value.[in] double
- a: lower limit.[in] double
- b: upper limit.[in] double
- c: mode.
`c`
double stdlib_base_dists_geometric_logcdf( const double x, const double a, const double b, const double c );
$3
`c
#include "stdlib/stats/base/dists/triangular/logcdf.h"
#include "stdlib/constants/float64/eps.h"
#include
#include
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_logcdf( 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 );
}
}
`
*
Notice
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[triangular-distribution]: https://en.wikipedia.org/wiki/Triangular_distribution