Logarithm of Cumulative Distribution Function

Geometric distribution logarithm of cumulative distribution function.

The cumulative distribution function for a geometric random variable is

where 0 <= p <= 1 is the success probability. x denotes the number of failures before the first success.

Usage

var logcdf = require( '@stdlib/stats/base/dists/geometric/logcdf' );

logcdf( x, p )

Evaluates the logarithm of the cumulative distribution function for a geometric distribution with success probability p.

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.

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.

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 of a geometric distribution with success probability p

var mylogcdf = logcdf.factory( 0.5 );
var y = mylogcdf( 3.0 );
// returns ~-0.065

y = mylogcdf( 1.0 );
// returns ~-0.288

Notes

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.

Examples

var randu = require( '@stdlib/random/base/randu' );
var logcdf = require( '@stdlib/stats/base/dists/geometric/logcdf' );

var p;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 5.0;
    p = randu();
    y = logcdf( x, p );
    console.log( 'x: %d, p: %d, ln(F(x;p)): %d', x.toFixed( 4 ), p.toFixed( 4 ), y.toFixed( 4 ) );
}