The domain of the beta distribution as defined in R is 0 <= x <= 1 and as shown by David Winsemius it is undefined outside [0,1]. But thats sort of the question I have. To elaborate, I have a variable with 0 as its natural lower limit but can assume any positive number as an upper limit. So its domain is [0, Inf]. In stead of the the two-parameter beta distribution with domain [0,1], I need to estimate a three parameter beta distribution with domain [0, max]. Given the parameter estimates for the 3-parameter distribution, I want to do the integration for two ranges say [0,d] and [d, Inf] for 0 < d < Inf. But the estimated distribution has a max < Inf and hence the same problem as in the example arises when I do the integration for [d, Inf]. Replacing the Inf with the estimated Max seem to work in some cases but not in others. Ravi Varadhan said such replacement doesn't make sense and in that case what can I do to implement the numerical integration in [d, Inf] using the estimated Beta distribution?
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