Below is a histogram of some data, the bins are integers the other parameters are irrelevant.
As you can see there seems to be two separate but overlapping normal distributions for odd and even numbers.
The probability of being an even number is 1/3, likewise 2/3 for an odd number.
I have no idea of actual statistical significance of this to be honest so I'm trying to find out what it even is to learn more, but I can't find anything, I've tried so many search terms to find this and even reverse image searches but all I get is information about multimodal distributions etc. and I can't find anything about when the multimodal distributions actually overlap in this manner
Is there a name for this?
For those interested the data is from 1,000,000 randomized games of goofspiel (N=13) using the matlab script
N = 1000000; random = zeros(1,N); for i = 1 : N pc = randperm(13); p1 = randperm(13); p2 = randperm(13); random(i) = sum(pc.*sign(p1-p2)); end histogram(random,'BinMethod','integer')
A more general (though artificial) example would be the following
a = [1:50 50:-1:1]; b = normpdf(linspace(-2,2),0,0.5).*50; c = a; rng('default') %For reproducibility d = logical(randi([0,1],1,length(a))); for i = 1:length(c) %There's gotta be a way to do this without an explicit loop if(d(i)) c(i) = b(i); end end bar(c)
Like the first example there's two distributions overlapped (triangular and normal), but in this case instead of alternating at each point, it's random.
I know this is an exaggerated example (and not even a histogram) but there has to be examples of this sort of thing actually happening with statistical data right? Then again maybe not, or it's completely irrelevant?
The actual question is two-fold:
The general question - What is this type of "thing" called, if anything? - so that I (or anyone else that might come across it) can learn more about it and if any adjustments need to be made.
The question as it specifically relates to my first dataset - should I separate the odd and even values or fit a normal distribution to the whole set?