I’d like to use a customized
Weibull distribution for the likelihood function which is not that different from its original from.
The general form of
Weibull distribution is expressed as follow:
A custom Weibull distribution I want to use has just one more location parameter l as follows:
Here, all the parameters \alpha, \beta, l have
Gamma distribution as their priors.
The shape and scale parameters of
Gamma are defined in a deterministic way.
In this case, what is the best way to model this?
I know how to use
as_op operator but I’d rather not to use it because I can’t use some gradient based sampler.
I’ve checked there is
pm.DensityDist to define a custom distribution but it’s capability seems somewhat limited and I couldn’t find a comprehensive guide to use
If the custom Weibull I mentioned above can be modeled by
pm.DensityDist, would you please give me some guide to define this?
If it is not possible to model using
pm.DensityDist then other advice would be appreciated very much.