# npm

## @stdlib/stats-base-dists-triangular-logcdf

0.0.7 • Public • Published

# 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.

## Installation

`npm install @stdlib/stats-base-dists-triangular-logcdf`

## Usage

`var logcdf = require( '@stdlib/stats-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```

## 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

```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 ) );
}```

## Notice

This package is part of 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, see the main project repository.

### Install

`npm i @stdlib/stats-base-dists-triangular-logcdf`

stdlib.io

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0.0.7

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