public abstract class NumericQuantile(T) : Quantile!T
Class to compute quantile function as root of it's cumulative density function. Unstable algorithm.
Example
Numeric quantile function of standard normal distribution
import std.traits, std.mathspecial;
import atmosphere.pdf;
import atmosphere.cdf;
class NormalPDF : PDF!real
{
real opCall(real x)
{
// 1/sqrt(2 PI)
enum c = 0.398942280401432677939946L;
return c * exp(-0.5f * x * x);
}
}
class NormalCDF : NumericCDF!real ///$(RED Unstable) algorithm.
{
this()
{
super(new NormalPDF, [-3, -1, 0, 1, 3]);
}
}
class NormalQuantile : NumericQuantile!real ///$(RED Unstable) algorithm.
{
this()
{
super(new NormalCDF);
}
}
auto qf = new NormalQuantile;
assert(approxEqual(qf(0.3), normalDistributionInverse(0.3)));
Example
Numeric quantile function of Generalized Hyperbolic distribution
import atmosphere.pdf;
import atmosphere.cdf;
import atmosphere.params;
import atmosphere.moment;
class GHypCDF: NumericCDF!real ///$(RED Unstable) algorithm.
{
this(real lambda, GHypChiPsi!real params)
{
immutable mu = 0;
auto pdf = new GeneralizedHyperbolicPDF!real(lambda, params.alpha, params.beta, params.delta, mu);
immutable mean = generalizedHyperbolicMean!real(lambda, params.beta, params.chi, params.psi);
super(pdf, [mean]);
}
}
class GHypQuantile : NumericQuantile!real ///$(RED Unstable) algorithm.
{
this(real lambda, GHypChiPsi!real params)
{
super(new GHypCDF(lambda, params), -1000, 1000);
}
}
auto qf = new GHypQuantile(0.5, GHypChiPsi!real(5, 0.7, 0.6));
import std.stdio, std.conv;
assert(approxEqual(qf(0.95), 40.9263));
assert(approxEqual(qf(0.99), 64.977));
public this(
CDF!T cdf,
T a = -T.max,
T b = T.max)
Constructor
Parameters
| cdf | The CDF to to inverse. |
| a | (optional) The lower bound. |
| b | (optional) The upper bound. |
public final T opCall(T x)
Call operator
Contracts
in
{
assert (x >= 0);
assert (x <= 1);
}
out (result)
{
assert (!result.isNaN);
}