two-sided censored model in R (similar to Zeligs Tobit)?

Is there a model for dependent variables that are censored on both sides? And if so is there an implementatio开发者_StackOverflown in R? I am only aware of tobit models (e.g. in Zelig package), but they´re obviously only censored on the left side... I wonder if it even makes sense to truncate on both sides...

1. There's a difference between truncation and censoring. You need to be aware of which is the case before you start modeling. (in a nutshell: Censoring means events can be detected, but the measurements are not known completely (i.e. in your case you neither know the exact beginning nor the exact end of the time interval subjects were under risk for the event you're considering). Truncation means events can be observed only if another condition is fullfilled: a popular example is survival in a retirement home that only accepts people over 65 to take up residence - entry into the study population is then truncated at age 65.)

2. if you have both left- and right censored data or data that are simultaneously right- and left-censored, the techncal term you are looking for is interval censored. ?Surv in package survival will show you how to define interval censored observations for modelling time-to-event in that case.

In a very real sense most of the observational studies on "free-range human" populations are doubly censored... i.e. we do not observe the individuals over all of their lifespans. Here is a citation to a PhD thesis that seems to lay out the statistical terminology well. Furthermore, several of the packages in R will function properly when set up for interval censoring or left-censoring, including packages survival, NADA, sand (from their DOE website) and several others for which you can search at Baron's website with appropriate search strategies in this link that sets up that page to get both functions and r-help entries.

Edit: Adding comments to address the clarification that this is about truncation rather than censoring.

If one is looking to fit to truncated distributions then look at the gamlss package, or create a suitable density for a doubly-truncated distribution and use fitdistr in the MASS package.