Random Variate from a transformed Distribution

Question

I would like to simulate random variates from a transformed distribution of a joint distribution and a constant.

i.e.

joint=ProductDistribution[NormalDistribution[],BetaDistribution[1,2],BetaDistribution[2,2]];
transform=TransformedDistribution[3*joint....]

I am unsure how to complete the transformed distribution code to put in the variables.

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score 1 · Accepted Answer · answered Dec 21 '14 at 23:12

1

joint = ProductDistribution[NormalDistribution[], BetaDistribution[1, 2], BetaDistribution[2, 2]];
q = TransformedDistribution[{x, y, z} w, {{x, y, z} \[Distributed]  joint, 
                                          w \[Distributed] UniformDistribution[]}]
ListPlot3D@RandomVariate[joint, 100]

Mathematica graphics

answered Dec 21 '14 at 23:12

Dr. belisarius

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Thanks for the help. Am I allowed to just say w is distributed by 3? I have an exact constant I would like to use. – Jim Dec 21 '14 at 23:14
@Jim Sorry, I don't understand what you mean by "w is distributed by 3" – Dr. belisarius Dec 21 '14 at 23:26

score 1 · Answer 2 · edited Apr 13 '17 at 12:55

1

joint = ProductDistribution[NormalDistribution[], BetaDistribution[1, 2], BetaDistribution[2, 2]];
td = TransformedDistribution[3 {x, y, z} , Distributed[{x, y, z}, joint]];

Through@{Mean, Variance}@td
(* {{0,1,3/2}, {9,1/2,9/20}} *)

PDF[td, {x, y, z}]

enter image description here

ListPlot3D[RandomVariate[td, 50]]

enter image description here

See also: this answer to a closely related question by the same OP.

edited Apr 13 '17 at 12:55

Community

1

answered Dec 22 '14 at 09:38

kglr

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Random Variate from a transformed Distribution

2 Answers2