# Product of univariate distributions
**URL:** https://discourse.julialang.org/t/product-of-univariate-distributions/1350
**Category:** Statistics
**Created:** [January 8, 2017, 2:27am UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350 "2017-01-08T02:27:59Z")
**Posts on this page:** 14
**Page:** 1
### Author:  [@nbren12](https://discourse.julialang.org/u/nbren12)
#### Post date: [January 8, 2017, 2:27am UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/1 "2017-01-08T02:27:59Z")
In Distributions.jl is it possible to create a cartesian product distribution, given two univariate random variables? I want to do this to make a multivariate uniform distribution supported over [0,1]\times[0,1]
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### Author:  [@johnmyleswhite](https://discourse.julialang.org/u/johnmyleswhite)
#### Post date: [January 8, 2017, 2:28am UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/2 "2017-01-08T02:28:54Z")
There’s no tooling for this at the moment, but there are several issues describing it. It’s pretty easy to use the existing distributions code as a template to create a new distribution.
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### Author:  [@nbren12](https://discourse.julialang.org/u/nbren12)
#### Post date: [January 8, 2017, 3:01am UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/3 "2017-01-08T03:01:57Z")
Ok. Understood. Thanks.
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### Author:  [@gragusa](https://discourse.julialang.org/u/gragusa)
#### Post date: [January 8, 2017, 1:55pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/4 "2017-01-08T13:55:11Z")
I have a small package implementing this that I use for MC where the product distribution is the prior. [BayesianTools.jl](https://github.com/gragusa/BayesianTools.jl). There is no documentation at the moment, but the test directory has the basic use cases.
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### Author:  [@nbren12](https://discourse.julialang.org/u/nbren12)
#### Post date: [January 8, 2017, 3:16pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/5 "2017-01-08T15:16:03Z")
yes! this seems like exactly what I need. Thanks. I just wanted to make a
multi-dimensional uniform distribution for MC.
-Noah
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### Author:  [@gragusa](https://discourse.julialang.org/u/gragusa)
#### Post date: [January 10, 2017, 4:42pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/6 "2017-01-10T16:42:41Z")
@nbren12 Since you were interested in this, I put some effort to update the package, include more thorough testing, and add a brief documentation. Let me know if this is useful to you and how can be improved.
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [January 10, 2017, 4:51pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/7 "2017-01-10T16:51:42Z")
Isn’t sampling from a multi-dimensional uniform distribution just given by
```julia
n = 3 # dimension
x = rand(n)
```
?
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [January 10, 2017, 5:06pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/8 "2017-01-10T17:06:43Z")
I guess you might want different ranges in different dimensions though.
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### Author:  [@nbren12](https://discourse.julialang.org/u/nbren12)
#### Post date: [January 10, 2017, 5:59pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/9 "2017-01-10T17:59:00Z")
@dpsanders
Distributions.jl does more than just sampling. It stores the pdf and other info which are necessary for doing things like Bayesian statistics.
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### Author:  [@nbren12](https://discourse.julialang.org/u/nbren12)
#### Post date: [January 10, 2017, 6:09pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/10 "2017-01-10T18:09:20Z")
Thanks! I will definitely take a closer look
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### Author:  [@dpsanders](https://discourse.julialang.org/u/dpsanders)
#### Post date: [January 10, 2017, 6:21pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/11 "2017-01-10T18:21:52Z")
Right, but everything is very trivial in the particular case of uniform distributions.
Certainly for non-uniform distributions, something more would be useful – maybe it could be refactored out of `BayesianTools.jl` into a separate package or part of `Distributions.jl`? cc @gragusa
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### Author:  [@johnmyleswhite](https://discourse.julialang.org/u/johnmyleswhite)
#### Post date: [January 10, 2017, 6:35pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/12 "2017-01-10T18:35:07Z")
We’ve got some issues about this product idea for Distributions. The main difficulty is whether you want to support arrays or tuples. I prefer tuples because you can handle heterogeneous types, but that creates other issues.
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### Author:  [@gragusa](https://discourse.julialang.org/u/gragusa)
#### Post date: [January 10, 2017, 7:10pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/13 "2017-01-10T19:10:56Z")
Yes I struggle with this myself. I just went for tuples because it seemed more natural and handle heterogeneity (alternatively you could go with generated functions, but it seems overkill to me). I just put this together because I needed it and I am not claiming that this is the best implementation — I just find this useful for the MCMC stuff I do.
@dpsanders happy to factor out whathever it is relevant
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### Author:  [@baggepinnen](https://discourse.julialang.org/u/baggepinnen)
#### Post date: [February 18, 2018, 6:27pm UTC](https://discourse.julialang.org/t/product-of-univariate-distributions/1350/14 "2018-02-18T18:27:27Z")
I am interested in learning if there has been any progress on product distributions in Distributions.jl or `BayesianTools.ProductDistributions`l is still the way to go?