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st: pdf of sum of ratios of normal distributions

From   Romain Espinosa <>
Subject   st: pdf of sum of ratios of normal distributions
Date   Tue, 3 Apr 2012 19:22:45 +0200

Hi everyone,

I have a question concerning the following model. I have J variables
X_j that are normally distributed with mean Delta_j and standard error
Sigma_j. I would like to compute the PDF of the following:

sum_(j!=k) (X_k)/(X_j) which is equivalent to : X_k/X_1 + X_k/X_2 ...
+ X_k/X_(k-1) + X_k/X_(k+1)+ ... + X_k/X_J.

I haven't found any user-written program so far (even for the ratio of
two normal distributions).  I would like to construct a program for
the probability density function with parameters (Delta_j)_(j=1...J),
(Sigma_j)_(j=1...J). I would use it afterwards to write a Maximum
Likelihood Program.

Thanks for your consideration.

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