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README.md |
Logarithm of Cumulative Distribution Function
Evaluate the natural logarithm of the cumulative distribution function for a beta prime distribution .
The cumulative distribution function for a beta prime random variable is
where alpha > 0
is the first shape parameter, beta > 0
is the second shape parameter and I
is the incomplete beta function.
Usage
var logcdf = require( '@stdlib/stats/base/dists/betaprime/logcdf' );
logcdf( x, alpha, beta )
Evaluates the natural logarithm of the cumulative distribution function (CDF) for a beta prime distribution with parameters alpha
(first shape parameter) and beta
(second shape parameter).
var y = logcdf( 0.5, 1.0, 1.0 );
// returns ~-1.099
y = logcdf( 0.5, 2.0, 4.0 );
// returns ~-0.618
y = logcdf( 0.2, 2.0, 2.0 );
// returns ~-2.603
y = logcdf( 0.8, 4.0, 4.0 );
// returns ~-0.968
y = logcdf( -0.5, 4.0, 2.0 );
// returns -Infinity
y = logcdf( +Infinity, 4.0, 2.0 );
// returns 0.0
If provided NaN
as any argument, the function returns NaN
.
var y = logcdf( NaN, 1.0, 1.0 );
// returns NaN
y = logcdf( 0.0, NaN, 1.0 );
// returns NaN
y = logcdf( 0.0, 1.0, NaN );
// returns NaN
If provided alpha <= 0
, the function returns NaN
.
var y = logcdf( 2.0, -1.0, 0.5 );
// returns NaN
y = logcdf( 2.0, 0.0, 0.5 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var y = logcdf( 2.0, 0.5, -1.0 );
// returns NaN
y = logcdf( 2.0, 0.5, 0.0 );
// returns NaN
logcdf.factory( alpha, beta )
Returns a function for evaluating the natural logarithm of the cumulative distribution function for a beta prime distribution with parameters alpha
(first shape parameter) and beta
(second shape parameter).
var mylogcdf = logcdf.factory( 0.5, 0.5 );
var y = mylogcdf( 0.8 );
// returns ~-0.767
y = mylogcdf( 0.3 );
// returns ~-1.143
Notes
- In virtually all cases, using the
logpdf
orlogcdf
functions is preferable to manually computing the logarithm of thepdf
orcdf
, respectively, since the latter is prone to overflow and underflow.
Examples
var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var logcdf = require( '@stdlib/stats/base/dists/betaprime/logcdf' );
var alpha;
var beta;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu();
alpha = ( randu()*5.0 ) + EPS;
beta = ( randu()*5.0 ) + EPS;
y = logcdf( x, alpha, beta );
console.log( 'x: %d, α: %d, β: %d, ln(F(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}