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I want to estimate the shape (alpha) parameter for a Pareto distribution. (We assume that we know the scale parameter =1 ).

The prior is alpha = 2 (and maybe we have always to assume a distribution ? if so, let's say that it is a normal law with mean=2 and sd=0.1).

With we have observations, for example (5,6,9,12,59,4)

Form these data, can we calculate a posterior ?

  • maybe we have to give a distribution for likelihood ? Let's say that it is a uniform law
  • or in the case of pareto law, we have some typical distribution ?

edit: Xi'an indicated that this question is solved with this question Conjugated priors (Pareto and Beta), name of the unconditional distribution?, but I can't see how. Could you please give a numerical solution.

alpha=rnorm(1000,2,0.1)
obs=c(5,6,9,12,59,4)
#....
post=?
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