GeneralContinuousDistribution Class

public class GeneralContinuousDistribution : UnivariateContinuousDistribution

Public Class GeneralContinuousDistribution
	Inherits UnivariateContinuousDistribution

// Let's suppose we have a formula that defines a probability distribution
// but we dont know much else about it. We don't know the form of its cumulative
// distribution function, for example. We would then like to know more about
// it, such as the underlying distribution's moments, characteristics, and 
// properties.

// Let's suppose the formula we have is this one:
double mu = 5;
double sigma = 4.2;

Func>double, double> df = x => 1.0 / (sigma * Math.Sqrt(2 * Math.PI))
                * Math.Exp(-Math.Pow(x - mu, 2) / (2 * sigma * sigma));

// And for the moment, let's also pretend we don't know it is actually the
// p.d.f. of a Gaussian distribution with mean 5 and std. deviation of 4.2.

// So, let's create a distribution based _solely_ on the formula we have:
var distribution = GeneralContinuousDistribution.FromDensityFunction(df);

// Now, we can check everything that we can know about it:

double mean = distribution.Mean;     // 5      (note that all of those have been
double median = distribution.Median; // 5       detected automatically simply from
double var = distribution.Variance;  // 17.64   the given density formula through
double mode = distribution.Mode;     // 5       numerical methods)

double cdf = distribution.DistributionFunction(x: 1.4);           // 0.19568296915377595
double pdf = distribution.ProbabilityDensityFunction(x: 1.4);     // 0.065784567984404935
double lpdf = distribution.LogProbabilityDensityFunction(x: 1.4); // -2.7213699972695058

double ccdf = distribution.ComplementaryDistributionFunction(x: 1.4); // 0.80431703084622408
double icdf = distribution.InverseDistributionFunction(p: cdf);       // 1.3999999997024655

double hf = distribution.HazardFunction(x: 1.4);            // 0.081789351041333558
double chf = distribution.CumulativeHazardFunction(x: 1.4); // 0.21776177055276186