Quantile Function

Exponential distribution quantile function.

The quantile function for an exponential random variable is

upper Q left-parenthesis p semicolon lamda right-parenthesis equals StartFraction minus ln left-parenthesis 1 minus p right-parenthesis Over lamda EndFraction

for 0 <= p <= 1, where λ is the rate parameter.

Usage

var quantile = require( '@stdlib/math/base/dists/exponential/quantile' );

quantile( p, lambda )

Evaluates the quantile function for a exponential distribution with rate parameter lambda.

var y = quantile( 0.5, 0.1 );
// returns ~6.931

y = quantile( 0.2, 4.0 );
// returns ~0.558

If provided a probability p outside the interval [0,1], the function returns NaN.

var y = quantile( 1.9, 1.0 );
// returns NaN

y = quantile( -0.1, 1.0 );
// returns NaN

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

var y = quantile( NaN, 1.0 );
// returns NaN

y = quantile( 0.0, NaN );
// returns NaN

If provided lambda < 0, the function returns NaN.

var y = quantile( 0.4, -1.0 );
// returns NaN

quantile.factory( lambda )

Returns a function for evaluating the quantile function of an exponential distribution with rate parameter lambda.

var myquantile = quantile.factory( 4.0 );

var y = myquantile( 0.2 );
// returns ~0.056

y = myquantile( 0.9 );
// returns ~0.576

Examples

var randu = require( '@stdlib/random/base/randu' );
var quantile = require( '@stdlib/math/base/dists/exponential/quantile' );

var lambda;
var p;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    p = randu();
    lambda = randu() * 10.0;
    y = quantile( p, lambda );
    console.log( 'p: %d, λ: %d, Q(p;λ): %d', p.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) );
}