Probability Distributions

ProbabilityDistributions is a collection of static helpers for drawing samples from common continuous distributions: normal (Gaussian), Cauchy, and uniform. It is used most prominently by the Nucleation module when seeding nucleus radii according to the $Distribution_<a>_<b> mode.

Key Classes and Concepts

• ProbabilityDistributions (static class / namespace under include/Tools/ProbabilityDistributions.h):
  • Normal (Gaussian): $\mathcal{N}(\mu ,\sigma )$
  • Cauchy (Lorentzian): $\mathrm{Cauchy}(\mu ,\gamma )$
  • Uniform: $U[a,b]$

Usage

Input

None. The distribution parameters come from the caller — for nucleation, from the $Center_<a>_<b>, $Deviation_<a>_<b>, $HalfWidth_<a>_<b>, $SeedRadiusMIN_<a>_<b>, $SeedRadiusMAX_<a>_<b> keys documented on Nucleation.

Output

None — pure sampling helpers.

Example

#include "Tools/ProbabilityDistributions.h"

// Sampling a normal distribution:
double r = ProbabilityDistributions::Normal(mu, sigma, rng);

// Uniform:
double u = ProbabilityDistributions::Uniform(rmin, rmax, rng);

(Function signatures follow whatever is declared in the header — the canonical consumer is Nucleation::Nucleate.)

Dependencies

• Nucleation — primary consumer.
• Standard C++ <random> machinery is used internally.