Group Abstract

Message Boards

WOLFRAM COMMUNITY

36 Views

4 Replies

1 Total Like

View groups...

Follow this post

Share this post:

GROUPS:

Wolfram Language Statistics and Probability

Transformed distribution assumptions

Patrick McMullen

Patrick McMullen, Wake Forest University

Posted 1 day ago

I am working with the TransformedDistribution function, and have successfully derived PDF functions for r, theta and phi. When I try and calculate the PDF for z = r * Cos[theta] via the TransformedDistribution function, I get stuck. My gut tells me that there is an assumption missing, but I am not sure. I need the PDF for the interval 0 < t < 2. My work is attached. Any suggestions? Attachments: Derivation.nb

POSTED BY: Patrick McMullen

4 Replies

Sort By:

Jim Baldwin

Posted 43 minutes ago

Following Gianluca Gorni's suggestion: disttheta = TransformedDistribution[ArcCos[2v - 1], v \[Distributed] UniformDistribution[{0, 1}]] distr = TransformedDistribution[v^(1/3), v \[Distributed] UniformDistribution[{0, 1}]] distphi = TransformedDistribution[v, v \[Distributed] UniformDistribution[{0, 2Pi}]] distz = TransformedDistribution[u*Cos[v], {u \[Distributed] distr, v \[Distributed] disttheta}] PDF[distz, z]

Following Gianluca Gorni's suggestion:

disttheta = TransformedDistribution[ArcCos[2*v - 1], v \[Distributed] UniformDistribution[{0, 1}]]
distr = TransformedDistribution[v^(1/3), v \[Distributed] UniformDistribution[{0, 1}]]
distphi = TransformedDistribution[v, v \[Distributed] UniformDistribution[{0, 2*Pi}]]
distz = TransformedDistribution[u*Cos[v], {u \[Distributed] distr, v \[Distributed] disttheta}]
PDF[distz, z]

PDF for z