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About stdlib...

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Logarithm of Cumulative Distribution Function

NPM version Build Status Coverage Status

Triangular distribution logarithm of cumulative distribution function.

The cumulative distribution function for a triangular random variable is

F ( x ; a , b , c ) = { 0 for  x a ( x a ) 2 ( b a ) ( c a ) for  a < x c 1 ( b x ) 2 ( b a ) ( b c ) for  c < x < b 1 for  b x

where a is the lower limit, b is the upper limit, and c is the mode.

Usage

To use in Observable,

logcdf = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-triangular-logcdf@umd/browser.js' )

To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:

var logcdf = require( 'path/to/vendor/umd/stats-base-dists-triangular-logcdf/index.js' )

To include the bundle in a webpage,

<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-triangular-logcdf@umd/browser.js"></script>

If no recognized module system is present, access bundle contents via the global scope:

<script type="text/javascript">
(function () {
    window.logcdf;
})();
</script>

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

<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-triangular-logcdf@umd/browser.js"></script>
<script type="text/javascript">
(function () {

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 ) );
}

})();
</script>
</body>
</html>

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.

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.