I have 100 observations $[z_0,…z_99]$ of a random variable $Z=X*Y$ which is a product of two normal random variables X and Y where $X~N(\mu_1,\sigma_1)$ and $Y~N(\mu_2,\sigma_2)$ with contraints $0<X<1$ and $0<Y<1$. I derived an integral representation for the pdf of Z but there is no analytical f…

[image] Vlad: I derived an integral representation for the pdf of Z Maybe you can try using this integral directly? eg: Custom theano Op to do numerical integration - #6 by aseyboldt

junpenglao, This is a different case as you have an integral representation for the location parameter $\mu$ while the likelihood is still Gaussian. In my case, i need to write the likelihood similar to formula 22 in http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-doi-10_71…

Likelihood for the product of two Gaussian random variables

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junpenglao February 16, 2018, 7:05am 2

Maybe you can try using this integral directly? eg: Custom theano Op to do numerical integration - #6 by aseyboldt

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Likelihood for the product of two Gaussian random variables

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