# ProbabilityDistribution with variable number of dimensions

I would like to construct a ProbabilityDistribution with a variable number of dimensions. I tried to use \$Assumptions = x ∈ Vectors[d, Reals] so that the variable x would be an unspecified vector with $$d$$ dimensions. However, I found that I could not use {x[[1]], -∞, ∞} to define the ranges of each element of the vector.

I'm seeking to define a distribution similar to the multivariate T distribution, but want flexibility to modify the definition. So I like to use ProbabilityDistribution for the definition, rather than using a built-in distribution.

My question is what's the best way to define a vector variable, which can be used in ProbabilityDistribution as a variable for the range of each dimensions defined?

• Something like: n = 3; ProbabilityDistribution[pdf, Sequence @@ Table[{x[i], -\[Infinity], \[Infinity]}, {i, n}]] ?
– JimB
Mar 8, 2019 at 17:28
• But I think that if you don't want to specify the dimension explicitly, then you'll probably need to do it with Product, Sum, etc. commands rather than ProbabilityDistribution. But I could certainly be wrong about that. Others can chime in. If leaving the dimensions unspecified is necessary, then maybe explaining why that's necessary would help someone make a constructive suggestion.
– JimB
Mar 8, 2019 at 18:55

n = 3;