Geometric distribution logarithm of cumulative distribution function (CDF).
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> [Geometric][geometric-distribution] distribution logarithm of [cumulative distribution function][cdf].
The [cumulative distribution function][cdf] for a [geometric][geometric-distribution] random variable is
where 0 <= p <= 1 is the success probability. x denotes the number of _failures_ before the first success.
``bash`
npm install @stdlib/stats-base-dists-geometric-logcdf
`javascript`
var logcdf = require( '@stdlib/stats-base-dists-geometric-logcdf' );
#### logcdf( x, p )
Evaluates the logarithm of the [cumulative distribution function][cdf] for a [geometric][geometric-distribution] distribution with success probability p.
`javascript
var y = logcdf( 2.0, 0.5 );
// returns ~-0.134
y = logcdf( 2.0, 0.1 );
// returns ~-1.306
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = logcdf( NaN, 0.5 );
// returns NaN
y = logcdf( 0.0, NaN );
// returns NaN
`
If provided a success probability p outside of [0,1], the function returns NaN.
`javascript
var y = logcdf( 2.0, -1.0 );
// returns NaN
y = logcdf( 2.0, 1.5 );
// returns NaN
`
#### logcdf.factory( p )
Returns a function for evaluating the logarithm of the [cumulative distribution function][cdf] of a [geometric][geometric-distribution] distribution with success probability p
`javascript
var mylogcdf = logcdf.factory( 0.5 );
var y = mylogcdf( 3.0 );
// returns ~-0.065
y = mylogcdf( 1.0 );
// returns ~-0.288
`
- In virtually all cases, using the logpmf or logcdf functions is preferable to manually computing the logarithm of the pmf or cdf, respectively, since the latter is prone to overflow and underflow.
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logcdf = require( '@stdlib/stats-base-dists-geometric-logcdf' );
var opts = {
'dtype': 'float64'
};
var p = uniform( 10, 0.0, 1.0, opts );
var x = uniform( 10, 0.0, 5.0, opts );
logEachMap( 'x: %0.4f, p: %0.4f, F(x;p): %0.4f', x, p, logcdf );
`
*
`c`
#include "stdlib/stats/base/dists/geometric/logcdf.h"
#### stdlib_base_dists_geometric_logcdf( x, p )
Evaluates the logarithm of the [cumulative distribution function][cdf] of a [geometric][geometric-distribution] distribution with success probability p.
`c`
double out = stdlib_base_dists_geometric_logcdf( 2.0, 0.5 );
// returns ~-0.134
The function accepts the following arguments:
- x: [in] double input value.[in] double
- p: probability of success.
`c`
double stdlib_base_dists_geometric_logcdf( const double x, const double p );
`c
#include "stdlib/stats/base/dists/geometric/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 x;
double p;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
x = random_uniform( 0.0, 40.0 );
p = random_uniform( 0.0, 1.0 );
y = stdlib_base_dists_geometric_logcdf( x, p );
printf( "x: %lf, p: %lf, ln(F(x;p)): %lf\n", x, p, 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
[geometric-distribution]: https://en.wikipedia.org/wiki/Geometric_distribution