I'd like to know how to impute non-normally distributed data from interval data, where the intervals differ across different individuals.
The variable I am interested in is the number of months an individual was unemployed in the three years after leaving full-time education. This variable is naturally bounded at 0-36.
I have partially observed working-histories for some individuals,though, so in some cases I can narrow this interval down. For example, I may observe an individual for 12 months and see they were unemployed in 3 of those months. Their interval can therefore be narrowed to 3-27.
These data are not normally distributed - they are heavily skewed towards zero, with a sizeable number of individuals at 36, too - due to truncation. (See picture below.)
Given this I think I should use predictive mean matching. I'd like to know if anyone knows of any method/software where the candidate pool of donors can be restricted based on the individuals' specific interval. Otherwise, I'm likely to impute values which I know to be false - i.e. outside the known bounds.
I know of programs which can use different bounds for different individuals, but these assume normally distributed data (e.g. ice package in Stata) or just truncate values afterwards if the imputed value is outside bounds (e.g. mice in R).
Does anyone have any suggestions please?