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Lévy distribution logarithm of cumulative distribution function.
The cumulative distribution function for a Lévy random variable is
where mu is the location parameter and b > 0 is the scale parameter.
npm install @stdlib/stats-base-dists-levy-logcdfvar logcdf = require( '@stdlib/stats-base-dists-levy-logcdf' );Evaluates the logarithm of the cumulative distribution function (CDF) for a Lévy distribution with parameters mu (location parameter) and c > 0 (scale parameter).
var y = logcdf( 2.0, 0.0, 1.0 );
// returns ~-0.735
y = logcdf( 12.0, 10.0, 3.0 );
// returns ~-1.51
y = logcdf( 9.0, 10.0, 3.0 );
// returns -InfinityIf 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 NaNIf provided c <= 0, the function returns NaN.
var y = logcdf( 2.0, 0.0, -1.0 );
// returns NaN
y = logcdf( 2.0, 0.0, 0.0 );
// returns NaNReturns a function for evaluating the logarithm of the cumulative distribution function of a Lévy distribution with parameters mu (location parameter) and c > 0 (scale parameter).
var mylogcdf = logcdf.factory( 3.0, 1.5 );
var y = mylogcdf( 4.0 );
// returns ~-1.511
y = mylogcdf( 2.0 );
// returns -Infinity- In virtually all cases, using the
logpdforlogcdffunctions is preferable to manually computing the logarithm of thepdforcdf, respectively, since the latter is prone to overflow and underflow.
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logcdf = require( '@stdlib/stats-base-dists-levy-logcdf' );
var mu;
var c;
var x;
var y;
var i;
for ( i = 0; i < 100; i++ ) {
mu = randu() * 10.0;
x = ( randu()*10.0 ) + mu;
c = ( randu()*10.0 ) + EPS;
y = logcdf( x, mu, c );
console.log( 'x: %d, µ: %d, c: %d, ln(F(x;µ,c)): %d', x.toFixed( 4 ), mu.toFixed( 4 ), c.toFixed( 4 ), y.toFixed( 4 ) );
}This package is part of 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, see the main project repository.
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