Identifying a mixture model I am trying to fit a mixture model to a dataset that consists of counts (so every record is a count of something, like the number of attempts by an IP address to connect to a website). I know, a priori, that each point belongs to one of two groups (for example malicious IPs and legitimate IPs), but I don't know which one without manually inspecting the record and determining the grouping. These are the things that I know though: 


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*As the count value increases, it is more and more likely that the data point belongs to group 2.

*80 percent of values are 1 and 85% are less than 2. 

*Most values for group 1 are 1, but there are values as high as 10,000 that are from group 1. 


Ideally, I'd like to be able to draw a line somewhere and say if the count is higher than some $n$, then I am $p$% sure that this record is from group 2. 
I think a mixture model is a good place to look at to model this data, but looking at the histogram and kernel density plot, I don't see any distinct clumps in data. Based on what I mentioned above, my guess is that a mixture of a log-logistic (for group 2) and pareto (for group 1) might be an ok approximation to the data. Is there an R package or python module that would estimate the parameters of such a mixture?     
 A: 
Ideally, I'd like to be able to draw a line somewhere and say if the count is higher than some n, then I am p% sure that this record is from group 2. 

It sounds like you want a model that gives an estimate of 
$P(Y=1|X=x)$
where $X$ is the variable representing the count, and $Y$ indicates membership of group 2 (Y=1 means "is a member").
When you say "A mixture of log-logistic and Pareto" it sounds like you're referring to $X$. But in the model, you condition on the value of $X$ so what its distribution is would be irrelevant (and strictly speaking, being a count, it can't be either log-logistic or Pareto since those are continuous) to that calculation.
There are a variety of tools for this job, but you might like to consider logistic regression as a first step. That will not require you to draw a line - it will give you an estimate of the probability at any $x$. If you want to pre-specify $p$, you can back out an estimate of the $x$ that corresponds to that $p$.

Is there an R package or python module that would estimate the parameters of such a mixture? 

This is such a different question as to merit its own post. In the first question you're modelling $Y|X=x$. Now it seems you want to deal with $X|Y=y$ ($y$ takes the values 0 and 1). Have I understood? You want a model that conditions the other direction?
