# How to create independent normal distribution variables in JuMP

**URL:** <https://discourse.julialang.org/t/how-to-create-independent-normal-distribution-variables-in-jump/116325>\
**Category:** Optimization (Mathematical)\
**Tags:** jump, optimization\
**Created:** [June 27, 2024, 8:20pm UTC](https://discourse.julialang.org/t/how-to-create-independent-normal-distribution-variables-in-jump/116325 "2024-06-27T20:20:30Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![SSGD](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@SSGD](https://discourse.julialang.org/u/SSGD)\
**Post date:** [June 27, 2024, 8:20pm UTC](https://discourse.julialang.org/t/how-to-create-independent-normal-distribution-variables-in-jump/116325/1 "2024-06-27T20:20:30Z")

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Hello 😃

I followed the [previous work](https://github.com/mlubin/JuMPChance.jl/blob/master/src/macros.jl) to define variables (normal distribution) in JuMP v.1.22.2 and want to use like this:

**@indepnormal(m\_chance, ω[i=1:numfarms], mean=0, var=farms[i].σ^2)**

But I met issues, following is my updated code:

> using Random
> 
> macro indepnormal(m, x, mean, var)  
> m = esc(m)  
> @assert isa(mean, Expr) && mean.head == :(=) && mean.args[1] == :mean  
> @assert isa(var, Expr) && var.head == :(=) && var.args[1] == :var  
> mean = esc(mean.args[2])  
> var = esc(var.args[2])
> 
> if isa(x, Symbol)  
> return quote  
> $(esc(x)) = IndepNormal($m, $mean, var, (string(x)))  
> nothing  
> end  
> else  
> if !(isa(x, Expr) && x.head == :ref)  
> error(“Syntax error: Expected $x to be of form var[…]”)  
> end
> 
> ```
> refcall = x.args[1]
> idxvars = x.args[2:end]
> variable = gensym(refcall)
> 
> idxvars_exprs = Expr[]
> for idxvar in idxvars
> push!(idxvars_exprs, :(for $(esc(idxvar)) in $(esc(refcall).args[2]) end))
> end
> 
> varname = string(refcall)
> varstr = :(string($varname, "["))
> 
> for idxvar in idxvars
> push!(varstr.args, :(string($(esc(idxvar)))))
> push!(varstr.args, ",")
> end
> deleteat!(varstr.args, length(varstr.args))
> push!(varstr.args, "]")
> 
> code = quote
> $(esc(refcall))[$(esc.(idxvars)...)] = IndepNormal($m, $mean, $var, $varstr)
> end
> 
> looped_code = code
> for (idxvar, idxset) in zip(idxvars, idxvars_exprs)
> looped_code = quote
> $idxset
> $looped_code
> end
> end
> 
> return quote
> $looped_code
> $esc(refcall) = $variable
> end
> 
> ```
> 
> end  
> end

Now an error shows: \*\*LoadError: LoadError: BoundsError: attempt to access 1-element Vector{Any} at index [2]. I don’t know how to make it work.

Any answer would be very appreciated. 🙏

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**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [June 27, 2024, 9:31pm UTC](https://discourse.julialang.org/t/how-to-create-independent-normal-distribution-variables-in-jump/116325/2 "2024-06-27T21:31:07Z")

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JuMPChance [GitHub - mlubin/JuMPChance.jl: A JuMP extension for probabilistic (chance) constraints](https://github.com/mlubin/JuMPChance.jl) is old archived code that does not support JuMP v1.22.

You should’t use it, and the code is probably not helpful to look at. I would strongly warn you against writing a macro; they are non-trivial to get right.

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**Author:** ![SSGD](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@SSGD](https://discourse.julialang.org/u/SSGD)\
**Post date:** [June 28, 2024, 8:04pm UTC](https://discourse.julialang.org/t/how-to-create-independent-normal-distribution-variables-in-jump/116325/3 "2024-06-28T20:04:50Z")

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Thank you @odow, I couldn’t agree more after so many days of trying.

Is there any way to add variables that follow a normal distribution in the JuMP model without writing a macro?

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**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [June 29, 2024, 12:11am UTC](https://discourse.julialang.org/t/how-to-create-independent-normal-distribution-variables-in-jump/116325/4 "2024-06-29T00:11:12Z")

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You cannot add variables that follow a normal distribution to a JuMP model.

If you want to solve a chance-constrained optimization problem, you will need to manually implement the reformulation.

The macro in JuMPChance was only a small user-facing feature. Most of the effort in the package was to automatically build the reformulations.

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<div class="post-metadata">

**Author:** ![SSGD](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@SSGD](https://discourse.julialang.org/u/SSGD)\
**Post date:** [June 29, 2024, 5:01pm UTC](https://discourse.julialang.org/t/how-to-create-independent-normal-distribution-variables-in-jump/116325/5 "2024-06-29T17:01:57Z")

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Thanks a lot @odow, now it’s clear.