Assume I have 100 observations, I know they are from two distribution functions, they are mixed together.

Is this possible to find out which distribution they are coming from?

Here is an example in R, 50 sample from a normal distribution, 50 sample from a uniform distribution.


a <- runif(50, min = -1, max = 1) # a is 50 sample from uniform distribution
b <- rnorm(50, mean = 0, sd = 1) # b is 50 sample form normal distribution

x <- c(a,b) # x is the mixed observation 

This is not a definite answer to your question, but might be of some help.

Alvarez-Esteban et al, in the paper Testing Similarity through Impartially Trimmed Wasserstein distances, discuss a data driven trimming method that maximizes the similarity between two distributions.

In your example, perhaps you can generate a sample S from a uniform distribution and compare this against your on data using their method. It will choose those points that maximize the similarity between the two distributions. This won't guarantee that you will get exactly the points you want, you might miss some, but may give you some idea of which ones are uniformly distributed. Their paper can be downloaded here. Perhaps would be nice to check some other papers from his team as well.


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