I've got discrete data (highest education level achieved to be exact, where each level has an associated integer, from 1 to 7, with a higher number corresponding to a higher education level). The two peaks I'm expecting (for my population) is at A-levels and having completed a degree. Between them is having started but not having finished a degree, which I'm not expecting a huge deal of my population to put as their highest level.
I'm after a discrete distribution, finite support (1,2,3,4,5,6,7,8), who's pmf follows the rough shape of a bimodal distribution. Does this exist? Can I just make one up?
I've never worked with real data before. When you're looking to assign a distribution to some data such as this (real life, messy, probably not entirely representative data) how do you go about fitting a distribution? Could anyone suggest reading material for this?