pareto.cpp File Reference

Pareto(xₘ, α) family implementation: scale (minimum) xₘ > 0, shape α > 0. More...

#include "DistributionCommon.h"
#include <algorithm>
#include <cmath>
#include <memory>
#include <optional>
#include <random>
#include <string>
#include <utility>
#include <vector>

Include dependency graph for pareto.cpp:

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Namespaces
namespace	provsql

Detailed Description

Pareto(xₘ, α) family implementation: scale (minimum) xₘ > 0, shape α > 0.

The canonical heavy-tailed power law (wealth, city / file sizes, insurance large losses). Raw moments are infinite for α <= j and reported as such (+Infinity, honestly) rather than estimated; the tail's self-similarity (X | X > a is Pareto(max(a, xₘ), α)) gives exact truncated moments and a rejection-free conditional sampler, and ln(X/xₘ) being Exp(α) gives a full cross-parameter comparator closed form – important because the tail is exactly where a uniform quadrature grid fails.

Self-contained family implementation: the class is file-local and reaches the evaluators only through the registrars at the bottom.

Definition in file pareto.cpp.