ProbabilityDist Class Reference

#include <probability.h>

Inheritance diagram for ProbabilityDist:
Component SIMDAlignedType DirectionSampler PositionSampler

Public Member Functions

 LM_INTERFACE_CLASS (ProbabilityDist, Component)
- Public Member Functions inherited from SIMDAlignedType
void * operator new (std::size_t size) throw (std::bad_alloc)
void operator delete (void *p)

Detailed Description

Probability distribution $P_X$ on the random variable $X$.

The inherited classes are expected to (implicitly) define

  • Probability space $(, F, P)$
  • Random variable
  • Probability space with the random variable $X$ : $({X}, {A}, )$

From the above information (and some additional assumptions) we can derive

  • CDF $F_X(E) = P(X^{-1}(X)), E {A}$
  • PDF $p_(x)$ defined by $P(X A) = {x A} p_(x) d(x), A F$