Hi.

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:

https://docs.pymc.io/api/distributions/continuous.html#pymc3.distributions.continuous.Weibull

f(x|\alpha,\beta)=\frac{\alpha}{\beta}(\frac{x}{\beta})^{\alpha-1}\mathrm{exp}(-(\frac{x}{\beta})^\alpha)

A custom Weibull distribution I want to use has just one more location parameter l as follows:

f(x|\alpha,\beta,l)=\frac{\alpha}{\beta}(\frac{x-l}{\beta})^{\alpha-1}\mathrm{exp}(-(\frac{x-l}{\beta})^\alpha)

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 `pm.DensityDist`

.

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.