As far as I know, Mathematica lacks a definition for a probability distribution representing a constant random variable.
Is this assertion correct?
Is there a problem in making such a distribution well-defined in Mathematica (assuming we treat it as a continuous rather than a discrete distribution)?
In principle, we could add definitions for this distribution, e.g.
CDF[ConstantDistribution[μ_]] ^:= UnitStep[# - μ] &
How would I find what definitions are needed to make it a "first class" member of the set of distributions supported by Mathematica? So that, for example, it could be used in functions such as
In general, there are ways to work around the lack of such a distribution, but just as it is sometimes useful to have a function such as
Identity (e.g. to pass to a function that transforms an input) it can be useful to have the "trivial" distribution.