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Topic: PDF for a LogLogNormal distribution
Replies: 1   Last Post: May 1, 1997 3:44 AM

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David E. Burmaster

Posts: 16
Registered: 12/7/04
PDF for a LogLogNormal distribution
Posted: Apr 29, 1997 9:48 PM
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I am stuck. I cannot find a way to use Mma to develop the PDF for a
probability distribution representing a random variable. Can you pls help


Let X be a Normal (or Gaussian) random variable with the usual PDF

PDF[X] = Normal[mu, sig]

= (sig Sqrt[2 Pi])^-1 Exp[-0.5 (x-mu)^2 sig^-2]


Now let Y = Exp[X] be a LogNormal random variable with the usual PDF

PDF[Y] = Exp[Normal[mu, sig] = LogNormal[mu, sig]

= (y sig Sqrt[2 Pi])^-1 Exp[-0.5 (Log[y]-mu)^2 sig^-2]

where mu and sig are the same parameters from PDF[X]


Now let Z = Exp[Y] = Exp[Exp[X]] be a LogLogNormal random variable

PDF[Z] = Exp[Exp[Normal[mu, sig]] = LogLogNormal[mu, sig]

=? some expression paramterized in mu and sig


Since Exp[] is a monotonic transformation, this should be "easy", but I
cannot elicit the answer from Mma.

Thank you for your help


David E. Burmaster, Ph.D.
Alceon Corporation (R)
PO Box 382669
Cambridge, MA 02238-2669

tel: 617-864-4300 x222
fax: 617-864-9954

(R) Alceon is a registered trademark of Alceon Corporation

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