Nonuniform PRNG?

[Sabrina Almodóvar]

On 07/12/2022 13:45, Stefan Ram wrote:

[...]

> |One of the oldest interpretations is the /limit frequency/
> |interpretation. If the conditioning event /C/ can lead 
> |to either A or "not A", and if in /n/ repetitions of such 
> |a situation the event A occurs /m/ times, then it is asserted
> |that P(A|C) = lim n-->oo (m/n). This provides not only 
> |an interpretation of probability, but also a definition 
> |of probability in terms of a numerical frequency ratio. 
> |Hence the axioms of abstract probability theory can 
> |be derived as theorems of the frequency theory. 
> |
> |In spite of its superficial appeal, the limit frequency
> |interpretation has been widely discarded, primarily because
> |there is no assurance that the above limit really exists for
> |the actual sequences of events to which one wishes to apply
> |probability theory.
> |
> "Quantum Mechanics" (1998) - Leslie E. Ballentine

That's pretty interesting.  Indeed, we really must discard this
frequency interpretation, even though it is what's in my mind when I
think of estimating the probability of a certain event, which I think
would be called the empirical distribution of probability?