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Wolfram Language Statistics and Probability

Slow Probability Density Function and Slow Density Plot

Patrick McMullen

Posted 14 days ago

I am doing some work with Random Variables and Probability Density Functions. I have entered the following commands: \[ScriptCapitalD] = TransformedDistribution[Abs[a - b] + Abs[u - v], {a \[Distributed] UniformDistribution[], b \[Distributed] UniformDistribution[], u \[Distributed] UniformDistribution[], v \[Distributed] UniformDistribution[]}] PDF[\[ScriptCapitalD], x] Everything works as it should, albeit slowly. When I ask for the plot via Plot[PDF[\[ScriptCapitalD], x], {x, -2, 4}, Filling -> Axis] things get super slow. Does anyone know what I am doing wrong?

I am doing some work with Random Variables and Probability Density Functions. I have entered the following commands:

\[ScriptCapitalD] = TransformedDistribution[Abs[a - b] + Abs[u - v], 
                             {a \[Distributed] UniformDistribution[],
                              b \[Distributed] UniformDistribution[],                                                                      
                              u \[Distributed] UniformDistribution[],
                              v \[Distributed] UniformDistribution[]}]

PDF[\[ScriptCapitalD], x]

Everything works as it should, albeit slowly. When I ask for the plot via

Plot[PDF[\[ScriptCapitalD], x], {x, -2, 4}, Filling -> Axis]

things get super slow.
Does anyone know what I am doing wrong?

POSTED BY: Patrick McMullen

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Jim Baldwin

Posted 14 days ago

I don't know what you mean by "slow". The following works after about 60 seconds: dist = TransformedDistribution[Abs[a - b] + Abs[u - v], {a \[Distributed] UniformDistribution[], b \[Distributed] UniformDistribution[], u \[Distributed] UniformDistribution[], v \[Distributed] UniformDistribution[]}]; Plot[Evaluate[PDF[dist, x]], {x, -2, 4}, Exclusions -> None, ImageSize -> Large]

I don't know what you mean by "slow". The following works after about 60 seconds:

dist = TransformedDistribution[Abs[a - b] + Abs[u - v],
   {a \[Distributed] UniformDistribution[], 
    b \[Distributed] UniformDistribution[],
    u \[Distributed] UniformDistribution[], 
    v \[Distributed] UniformDistribution[]}];
Plot[Evaluate[PDF[dist, x]], {x, -2, 4}, Exclusions -> None, ImageSize -> Large]

pdf

POSTED BY: Jim Baldwin

Patrick McMullen

Posted 13 days ago

Thank you, Jim. The Evaluation[] function inside the Plot[] function seems to have made the difference. I was not aware of this function, but now things work. Prior to this, I was waiting hours for the plot.

POSTED BY: Patrick McMullen

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