Counting the uncounted: How many were killed in Guatemala, 1978-1995?

In various application domains, there is a certain `null cell’, inside a multinomial setup, where observations are recorded for the other cells, but where one cannot count the number of occurrences for the null cell. I develop inference theory for assessing such unknown numbers, counting the uncounted, in situations where counts are available for the other cells, via parametric modelling. The methods are used to estimate the number of persons killed in Guatemala during the Genocidio guatemalteco years 1978–1995. There are three carefully curated lists of killed people, where the information can be mapped to a Venn diagram with $2^3=8$ cells. Summing over the seven observed cells, $R=\text{47,803}$ killed individuals can be identified, but how big is $N_{0,0,0}$, and hence $N=N_{0,0,0}+R$?