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Mathematics Mathematica Statistics and Probability

Quantile of a Transformed Distribution

Bruce Colletti

Posted 10 years ago

For independent discrete random variables X and Y uniformly distributed over {1,2,3,4,5}, I want to compute the 30th quantile of X + Y. Why doesn't the first block of code work (it simply echos back the Quantile command)? The second block works (a solution from Tech Support a few years ago). Thanks. Z = TransformedDistribution[X + Y, {X \[Distributed] DiscreteUniformDistribution@{1, 5}, Y \[Distributed] DiscreteUniformDistribution@{1, 5}}]; Quantile[Z, 0.3] Z = TransformedDistribution[X + Y, {X \[Distributed] DiscreteUniformDistribution@{1, 5}, Y \[Distributed] DiscreteUniformDistribution@{1, 5}}]; dist = ProbabilityDistribution[PDF[Z, x], {x, 2, 10, 1}]; Quantile[dist, .3]

For independent discrete random variables X and Y uniformly distributed over {1,2,3,4,5}, I want to compute the 30th quantile of X + Y. Why doesn't the first block of code work (it simply echos back the Quantile command)? The second block works (a solution from Tech Support a few years ago). Thanks.

Z = TransformedDistribution[X + Y,
      {X \[Distributed] DiscreteUniformDistribution@{1, 5},
        Y \[Distributed] DiscreteUniformDistribution@{1, 5}}];
Quantile[Z, 0.3]



Z = TransformedDistribution[X + Y,
      {X \[Distributed] DiscreteUniformDistribution@{1, 5},
        Y \[Distributed] DiscreteUniformDistribution@{1, 5}}];
dist = ProbabilityDistribution[PDF[Z, x], {x, 2, 10, 1}];
Quantile[dist, .3]

POSTED BY: Bruce Colletti