Natural logarithm of the cumulative distribution function (CDF) for a normal distribution.
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> Evaluate the natural logarithm of the cumulative distribution function (CDF) for a [normal][normal-distribution] distribution.
``bash`
npm install @stdlib/stats-base-dists-normal-logcdf
`javascript`
var logcdf = require( '@stdlib/stats-base-dists-normal-logcdf' );
#### logcdf( x, mu, sigma )
Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [normal][normal-distribution] distribution with parameters mu (mean) and sigma (standard deviation).
`javascript
var y = logcdf( 2.0, 0.0, 1.0 );
// returns ~-0.023
y = logcdf( -1.0, 4.0, 2.0 );
// returns ~-5.082
`
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 sigma < 0, the function returns NaN.
`javascript`
var y = logcdf( 2.0, 0.0, -1.0 );
// returns NaN
If provided sigma = 0, the function evaluates the natural 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, sigma )
Returns a function for evaluating the [cumulative distribution function][cdf] (CDF) of a [normal][normal-distribution] distribution with parameters mu (mean) and sigma (standard deviation).
`javascript
var mylogcdf = logcdf.factory( 10.0, 2.0 );
var y = mylogcdf( 10.0 );
// returns ~-0.693
y = mylogcdf( 5.0 );
// returns ~-5.082
`
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logcdf = require( '@stdlib/stats-base-dists-normal-logcdf' );
var opts = {
'dtype': 'float64'
};
var sigma = uniform( 10, 0.0, 20.0, opts );
var mu = uniform( 10, -5.0, 5.0, opts );
var x = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, µ: %0.4f, σ: %0.4f, ln(F(x;µ,σ)): %0.4f', x, mu, sigma, logcdf );
`
*
`c`
#include "stdlib/stats/base/dists/normal/logcdf.h"
#### stdlib_base_dists_normal_logcdf( x, mu, sigma )
Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [normal][normal-distribution] distribution with parameters mu (mean) and sigma (standard deviation).
`c`
double out = stdlib_base_dists_normal_cdf( 2.0, 0.0, 1.0 );
// returns ~-0.023
The function accepts the following arguments:
- x: [in] double input value.[in] double
- mu: mean.[in] double
- sigma: standard deviation.
`c`
double stdlib_base_dists_normal_logcdf( cconst double x, const double mu, const double sigma );
`c
#include "stdlib/stats/base/dists/normal/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 sigma;
double mu;
double x;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
x = random_uniform( 0.0, 10.0 );
mu = random_uniform( -5.0, 5.0 );
sigma = random_uniform( 0.1, 20.0 );
y = stdlib_base_dists_normal_logcdf( x, mu, sigma );
printf( "x: %lf, µ: %lf, σ: %lf, ln(F(x;µ,σ)): %lf\n", x, mu, sigma, y );
}
}
`
*
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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[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[normal-distribution]: https://en.wikipedia.org/wiki/Normal_distribution
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution