@stdlib/stats-base-dists-triangular-cdf
v0.3.1TypeScript
Triangular distribution cumulative distribution function (CDF).
stdlibstdmathstatisticsstatsdistributiondistprobabilitycdfcumulative distributiondistribution function
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Published by The Stdlib Authors
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Cumulative Distribution Function
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> [Triangular][triangular-distribution] distribution [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-cdf
Usage
`javascript`
var cdf = require( '@stdlib/stats-base-dists-triangular-cdf' );
#### cdf( x, a, b, c )
Evaluates 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 = cdf( 0.5, -1.0, 1.0, 0.0 );
// returns 0.875
y = cdf( 0.5, -1.0, 1.0, 0.5 );
// returns 0.75
y = cdf( -10.0, -20.0, 0.0, -2.0 );
// returns ~0.278
y = cdf( -2.0, -1.0, 1.0, 0.0 );
// returns 0.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = cdf( NaN, 0.0, 1.0, 0.5 );
// returns NaN
y = cdf( 0.0, NaN, 1.0, 0.5 );
// returns NaN
y = cdf( 0.0, 0.0, NaN, 0.5 );
// returns NaN
y = cdf( 2.0, 1.0, 0.0, NaN );
// returns NaN
`
If provided parameters not satisfying a <= c <= b, the function returns NaN.
`javascript
var y = cdf( 2.0, 1.0, 0.0, 1.5 );
// returns NaN
y = cdf( 2.0, 1.0, 0.0, -1.0 );
// returns NaN
y = cdf( 2.0, 0.0, -1.0, 0.5 );
// returns NaN
`
#### cdf.factory( a, b, c )
Returns a function for evaluating the [cumulative distribution function][cdf] of a [triangular][triangular-distribution] distribution with parameters a (lower limit), b (upper limit) and c (mode).
`javascript
var mycdf = cdf.factory( 0.0, 10.0, 2.0 );
var y = mycdf( 0.5 );
// returns 0.0125
y = mycdf( 8.0 );
// returns 0.95
`
Examples
`javascript
var randu = require( '@stdlib/random-base-randu' );
var cdf = require( '@stdlib/stats-base-dists-triangular-cdf' );
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 = cdf( x, a, b, c );
console.log( 'x: %d, a: %d, b: %d, c: %d, 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/triangular/cdf.h"
#### stdlib_base_dists_triangular_cdf( x, a, b, c )
Evaluates 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_triangular_cdf( 0.5, -1.0, 1.0, 0.0 );
// returns 0.875
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_triangular_cdf( const double x, const double a, const double b, const double c );
$3
`c
#include "stdlib/stats/base/dists/triangular/cdf.h"
#include "stdlib/constants/float64/eps.h"
#include
#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, 40.0 ) + STDLIB_CONSTANT_FLOAT64_EPS;
c = a + random_uniform( 0.0, b - a );
y = stdlib_base_dists_triangular_cdf( x, a, b, c );
printf( "x: %lf, a: %lf, b: %lf, c: %lf, 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].
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---
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