gamma(.., ..)^2 -> generalized_gamma(?, ?, ?)

[S]

Hello,

I have shape and rate parameters of a gamma distribution that seem to be related as some form of rate=shape^2

Now I want to observe if rate followes a generalized_gamma distribution. Howeve my dummy attempts for developing such function failed in test

I found the generalised gamma function in BUGS 

these are the attempts

#1

set.seed(1)   # for reproducible example

s = 50

r = 3

x <- rgamma(10000,shape=s,rate=r)

stan(

model_code="

functions{

real ggamma_lpdf(real x, real a, real b, real c) {

return( (c*a * (log (c) + log(b)) ) + ((c*a - 1) * log (x) ) + (-(b*x)^c ) - log( tgamma(a) ));

}

}

data {

int<lower=1> G;

vector[G] y; 

}

parameters { real<lower=0> h[3]; }

model { for(g in 1:G) y[g] ~ ggamma(h[1], h[2], h[3]); }

", 

data = list(G=length(x), y=x)

)

#2

set.seed(1)   # for reproducible example

s = 50

r = 3

x <- rgamma(10000,shape=s,rate=r)

stan(

model_code="

functions{

real ggamma_lpdf(real x, real a, real b, real c) {

return(log(c*b^(c*a) * x^(c*a - 1) * exp(-(b*x)^c) / tgamma(a)));

}

}

data {

int<lower=1> G;

vector[G] y; 

}

parameters { real<lower=0> h[3]; }

model { for(g in 1:G) y[g] ~ ggamma(h[1], h[2], h[3]); }

", 

data = list(G=length(x), y=x)

)

Thanks

[Bob Carpenter]

First thing to do is test your gamma implementations before
trying to fit.

It helps if you say how things failed.

Rather than log(tgamma(x)), you want lgamma(x).

It should look like this:

return log(c)
+ c * a * log(b)
+ (c * a - 1) * log(x)
- (b * x)^c
- lgamma(a);

then either use the function exposer in RStan or test within the
Stan program to make sure you get the right values using some kind
of independent implementation.

- Bob

> On May 12, 2017, at 8:43 PM, S <mangiol...@gmail.com> wrote:
>
> Hello,
>
> I have shape and rate parameters of a gamma distribution that seem to be related as some form of rate=shape^2
>
> Now I want to observe if rate followes a generalized_gamma distribution. Howeve my dummy attempts for developing such function failed in test
>
> I found the generalised gamma function in BUGS
>
>
>
>
>
>
>

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