How to choose a distribution for the likelihood step?

Questions
5

Welcome!

I guess it depends what you mean by a “reference”. But you can certain use a Weibull if you think that’s appropriate:

import arviz as az
import pymc as pm

with pm.Model() as model:
    alpha = pm.HalfNormal("alpha", sigma=5)
    beta = pm.HalfNormal("beta", sigma=5)
    likelihood = pm.Weibull(
        "likelihood", alpha=alpha, beta=beta, observed=[1, 2, 3, 4, 5, 6, 7, 8]
    )
    idata = pm.sample()

az.summary(idata)

yields:

        mean     sd  hdi_3%  hdi_97%  ...  mcse_sd  ess_bulk  ess_tail  r_hat
alpha  2.014  0.585   0.935    3.082  ...    0.010    1798.0    1825.0    1.0
beta   5.227  1.044   3.339    7.154  ...    0.017    1816.0    2048.0    1.0