@stdlib/stats-base-dists-logistic-logcdf
v0.3.1TypeScript
Logistic distribution logarithm of cumulative distribution function (CDF).
stdlibstdmathstatisticsstatsdistributiondistprobabilitycdfcumulative distributiondistribution function
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About stdlib...
Logarithm of Cumulative Distribution Function
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> [Logistic][logistic-distribution] distribution logarithm of [cumulative distribution function][cdf].
The [cumulative distribution function][cdf] for a [logistic][logistic-distribution] random variable is
where mu is the location parameter and s > 0 is the scale parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-logistic-logcdf
Usage
`javascript`
var logcdf = require( '@stdlib/stats-base-dists-logistic-logcdf' );
#### logcdf( x, mu, s )
Evaluates the logarithm of the [cumulative distribution function][cdf] (CDF) for a [logistic][logistic-distribution] distribution with parameters mu (location parameter) and s (scale parameter).
`javascript
var y = logcdf( 2.0, 0.0, 1.0 );
// returns ~-0.127
y = logcdf( 0.0, 0.0, 1.0 );
// returns ~-0.693
y = logcdf( -1.0, 4.0, 2.0 );
// returns ~-2.579
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = logcdf( NaN, 0.0, 1.0 );
// returns NaN
y = logcdf( 0.0, NaN, 1.0 );
// returns NaN
y = logcdf( 0.0, 0.0, NaN );
// returns NaN
`
If provided s < 0, the function returns NaN.
`javascript`
var y = logcdf( 2.0, 0.0, -1.0 );
// returns NaN
If provided s = 0, the function evaluates the logarithm of the [CDF][cdf] of a [degenerate distribution][degenerate-distribution] centered at mu.
`javascript
var y = logcdf( 2.0, 8.0, 0.0 );
// returns -Infinity
y = logcdf( 8.0, 8.0, 0.0 );
// returns 0.0
y = logcdf( 10.0, 8.0, 0.0 );
// returns 0.0
`
#### logcdf.factory( mu, s )
Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of a [logistic][logistic-distribution] distribution with parameters mu (location parameter) and s (scale parameter).
`javascript
var mylogcdf = logcdf.factory( 10.0, 2.0 );
var y = mylogcdf( 10.0 );
// returns ~-0.693
y = mylogcdf( 8.0 );
// returns ~-1.313
`
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 uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logcdf = require( '@stdlib/stats-base-dists-logistic-logcdf' );
var opts = {
'dtype': 'float64'
};
var x = uniform( 10, 0.0, 10.0, opts );
var mu = uniform( 10, 0.0, 10.0, opts );
var s = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, µ: %0.4f, s: %0.4f, ln(F(x;µ,s)): %0.4f', x, mu, s, logcdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/logistic/logcdf.h"
#### stdlib_base_dists_logistic_logcdf( x, mu, s )
Evaluates the logarithm of the cumulative distribution function (CDF) for a logistic distribution with location parameter mu and scale parameter s at a value x.
`c`
double out = stdlib_base_dists_logistic_logcdf( 2.0, 0.0, 1.0 );
// returns ~-0.127
The function accepts the following arguments:
- x: [in] double input parameter.[in] double
- mu: location parameter.[in] double
- s: scale parameter.
`c`
double stdlib_base_dists_logistic_logcdf( const double x, const double mu, const double s );
$3
`c
#include "stdlib/stats/base/dists/logistic/logcdf.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 mu;
double s;
double x;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
mu = random_uniform( -5.0, 5.0 );
s = random_uniform( 0.0, 20.0 );
x = random_uniform( -10.0, 10.0 );
y = stdlib_base_dists_logistic_logcdf( x, mu, s );
printf( "x: %lf, µ: %lf, s: %lf, ln(F(x;µ,s)): %lf\n", x, mu, s, 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]
---
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[branches-url]: https://github.com/stdlib-js/stats-base-dists-logistic-logcdf/blob/main/branches.md
[logistic-distribution]: https://en.wikipedia.org/wiki/Logistic_distribution
[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution