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I have data that is truncated on the left and censored on the right. The reason is that this is claims data, which for a claim gives the amount of the claim. The claim appears in the data:

  • Only if it exceeds a reporting threshold $\alpha$ (which is known) ;
  • If the amount exceeds a limit amount $\beta$ (which is known), then this amount $\beta$ is shown (instead of the true amount).

My goal is to find the best distribution among a set of distributions (exponential, gamma, beta, lognormal, normal, weibull, loglogistic, pareto, generalized pareto, etc.) according to a certain method (MME or MLE) and certain estimation criteria (SSE, etc.).

  1. Assume that $\beta=+\infty$ (i.e. no censoring). Does fitting a distribution or the equivalent truncated distribution gives the same result? I suppose not, but I don't really have any intuition about this.

  2. Let's assume $\beta<+\infty$ . Here it's very clear that the result will be different between original and censored distributions. But I don't really know how to make a censored distribution.

  3. So far I use the python library Fitter, but it does not allow to fit truncated or censored distributions. Is there another library (python, R or other) that allows to do this? I'd rather avoid having to implement all these fits myself.

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  • $\begingroup$ I presume "then this amount is shown" means "then the amount $\beta$ is shown"? Could you please edit the question to make that unambiguous? $\endgroup$
    – Stef
    Commented Aug 30, 2022 at 11:16
  • $\begingroup$ Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. $\endgroup$
    – Community Bot
    Commented Aug 30, 2022 at 11:41
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    $\begingroup$ @Stef it's done! $\endgroup$
    – Meth
    Commented Aug 30, 2022 at 11:58
  • $\begingroup$ The R package fitdistrplus can fit to censored data. I don't know if there's a Python equivalent. $\endgroup$
    – neilfws
    Commented Apr 25, 2023 at 23:56

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