My model involves solving an equation of the F(d, b e^{k}) = \frac{q}{c - 1} for b, where F(.) is the gamma CDF. Obviously, b = \frac{F^{-1}(\frac{q}{c - 1}, 1, d)}{e^{k}} , where F^{-1} is the inverse of the incomplete gamma quantile function. Is there a way to implement this in stan? The func…

Ah nvm, there was some issue with previous code. Checked again and it works :)

\frac{\delta F^{-1} (x; \alpha, \beta)}{\delta \beta} = -\frac{ Q^{-1} (x, \alpha, \beta)^{1-\alpha} (Q^{-1} (x, \alpha, \beta)^\alpha + \beta \Gamma(\alpha) exp(Q^{-1} (x, \alpha, \beta)) ) }{\beta^2} link to derivative The partial derivative with respect to \alpha is the same as the previous di…

That wolfram code isn’t what you’ve specified in the LaTeX, unfortunately. InverseGammaRegularized[a,q] is the same as gamma_q_inv(a,q), which isn’t want you want. Additionally, InverseGammaRegularized[a,q]/q is the inverse divided by x, not by \beta. The correct derivative is given by: D[Inverse…

Alright, so for the function: F^{-1}\left(x; \alpha, \beta \right) = \frac{Q^{-1}(\alpha,1-x)}{\beta} Which is given in Wolfram Alpha by InverseGammaRegularized[a,1-x]/b, and can be verified by comparing against qgamma(x,shape=a,rate=b). The partial derivatives for each input are given by: x:…

[image] andrjohns: #include <boost/math/special_functions/hypergeometric_pFq.hpp> #include <stan/math/prim/scal.hpp> #include <stan/math/rev/core.hpp> // Function to handle Stan parameters inline stan::math::var gamma_icdf(const stan::math::var& x, const stan::…

So after some more testing, it looks like including the Boost header (hypergeometric_pFq.hpp) is causing issues with rstan’s usage of other boost functions. The best way forward here is to use cmdstanr: R Interface to CmdStan • cmdstanr , which includes external c++ in a different way. Once you hav…

After several attempts I finally have cmdstan and cmdstanr installed. I tried running the codes below but ended up with Error 127 mingw32-make.exe: *** [make/program:47: C:\Users\lucp9544\AppData\Local\Temp\Rtmpa05r64\model-4714e0f2622.hpp] Error 127. I tried the bernoulli example which works fine. …

What happens if you run the script I posted above with no changes?

[image] andrjohns: library(cmdstanr) hpp = "#include <stan/math/prim.hpp> #include <stan/math/rev/core.hpp> #include <boost/math/special_functions/hypergeometric_pFq.hpp> // Function to handle Stan parameters inline stan::math::var gamma_icdf(const stan::math::var& x, …

Gamma distribution quantile and inverse quantile function

General

andrjohns June 9, 2021, 10:08pm 30

Can you post the stan_model call that you’re using and the result of calling cat on the Stan and C++ files?

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Gamma distribution quantile and inverse quantile function

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