I have a number of pricing datasets with integer values (prices in round dollars) for the same product which are right-censored at different levels (one level per dataset). I would like to combine those datasets in a single one to determine the c.d.f. of the prices for the product up to the maximum price observed.

As a note, these are monthly data, I have historical data for the same datasets for multiple months, and I want to find the distribution for the next month.

So, for example, one data set with 100 prices in [1,10] and 1000 > 10, another with 200 prices in [1,20] and 2000 > 20 and a third one with 20 prices in [1,30] and 200 in > 30.

For each of them I also know the total number of data, i.e. the total demand for the first data set is 1100, the second one 2200 and the third 220 (but we only see the first 100, 200, 20 due to right censoring).

The aim is to estimate a single c.d.f. (or p.m.f.) for each price in [1,30]. Note that in practice we have 10-100 such datasets for each product. I would like to do this in an automatic way, since we have a lot of such products.

The most naive thing that came in my mind because of my lack of statistical background is to get the c.d.f. of each dataset and then do some monotonic regression on the data. However this would not take into account the difference in the number of samples for each dataset.

Another way to combine the data could be to merge all the data in [1,10] from the three datasets, [1,20] from the first two datasets and in [1,30] only from the third dataset. But this would use some of the same data for each estimate.

My question is how could one merge the data and how to construct the c.d.f. Also any resources/books would be highly appreciated.

NOTE: The difference between this question and the one here is that all the data is censored and time-series data, so the aim is to predict next month's c.d.f. from the previous datasets.


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