I have a dataset with a pdf like in the attached image. There is a lower limit of detection on my measured data, but it doesn’t take on a precise value, hence the spike in data is a narrow distribution, but not a line. Instead of the data being censored, I have a lot of values close to the limit of detection. I assume there is some normal distribution in reality, that is being “truncated” by my measurement.

How would I deal with this in PyMC3? I’ve explored the bounded and truncated distributions, but those seem to deal moreso with censored data? There’s information contained in the proportion of the pdf that is in the limit of detection region, so I’d rather not just censor it. Thoughts?