Hello

I have a custom pdf to model in Stan. This is problem 16.3 in Ben Lambert’s newish book. The pdf is:

p(X)=[∛b/(Γ (4/3)]*[ exp(-b(X^3 )]

We are asked to estimate b,but there is a gamma function of a fraction(4/3) in the pdf which Stan doesn’t like.

My code:

```
functions{
real example_lpdf(real aX,real aMu){
return(log((1/(tgamma(4/3)))*(aMu^(1/3))*(exp(-aMu*(aX^3))))); //doesn't want to parse the gamma of a fraction
}
}
data{
int N;
real X[N];
}
parameters{
real b;
}
model{
for (i in 1:N){
X[i] ~ example(b);
}
b~normal(0,2); //this looks like where most of it would be
}
```

It runs if you leave the gamma function out, and still runs with it but gives odd results.The Stan manual says “gammat” should work with a positive number,but it wants to round the fraction to an integer.

Maybe gamma(4/3) simplifies to a function of pi,but I couldn’t see this anywhere.

The datatset (stan_survival.csv)for this problem is on the website for the book “A Student’s Guide to Bayesian Statistics” by Ben Lambert(Sage Publications).

Thanks for any advice.

Chris