Logarithm of Cumulative Distribution Function

Uniform distribution logarithm of cumulative distribution function.

The cumulative distribution function for a continuous uniform random variable is

upper F left-parenthesis x right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 0 2nd Column for x less-than a 2nd Row 1st Column StartFraction x minus a Over b minus a EndFraction 2nd Column for a less-than-or-equal-to x less-than b 3rd Row 1st Column 1 2nd Column for x greater-than-or-equal-to b EndLayout

where a is the minimum support and b is the maximum support. The parameters must satisfy a < b.

Usage

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

logcdf( x, a, b )

Evaluates the logarithm of the cumulative distribution function (CDF) for a uniform distribution with parameters a (minimum support) and b (maximum support).

var y = logcdf( 9.0, 0.0, 10.0 );
// returns ~-0.105

y = logcdf( 0.5, 0.0, 2.0 );
// returns ~-1.386

y = logcdf( -Infinity, 2.0, 4.0 );
// returns -Infinity

y = logcdf( +Infinity, 2.0, 4.0 );
// returns 0.0

If provided NaN as any argument, the function returns NaN.

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 a >= b, the function returns NaN.

var y = logcdf( 1.0, 2.5, 2.0 );
// returns NaN

logcdf.factory( a, b )

Returns a function for evaluating the logarithm of the cumulative distribution function of a uniform distribution with parameters a (minimum support) and b (maximum support).

var mylogcdf = logcdf.factory( 0.0, 10.0 );
var y = mylogcdf( 0.5 );
// returns ~-2.996

y = mylogcdf( 8.0 );
// returns ~-0.223

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

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

var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 25; i++ ) {
    x = (randu() * 20.0) - 10.0;
    a = (randu() * 20.0) - 20.0;
    b = a + (randu() * 40.0);
    y = logcdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, ln(F(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}
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