Comment #4 on issue 3129 by [email protected]: Drastic change to
sympy.stats: Adding concept of Probability Distributions on surface level
http://code.google.com/p/sympy/issues/detail?id=3129
I certainly agree with the general idea.
I think that the main trouble with sympy.stats is that its objects don't
map cleanly to established mathematical concepts. RandomSymbol does
represent random variables, but PSpace and RandomDomain are odd beasts.
So, having a representation of probability distributions should simplify
the design. The mathematical abstraction underlying them is the concept of
measure (https://en.wikipedia.org/wiki/Measure_theory), and a Measure
object mu would have one important method: mu.integrate(f, D) implementing
\int_D f dµ. Implementing only the counting
measure(https://en.wikipedia.org/wiki/Counting_measure) and the Lebesgue
measure(https://en.wikipedia.org/wiki/Lebesgue_measure) would unify the
discrete and continuous cases.
Note that for us, a measure and a measure space (or a probability
distribution and a probability space) are the same thing, since a measure
needs to "know" its domain of definition and thus has to contain all the
information that makes up a measure space.
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