>>13847746depends on what you mean. If you mean distributions in the statistics sense (guassian, exponential, Poisson, etc), those generally arise from math. For example, the normal distribution can be derived from some assumptions. Say you have some unknown quantity Y. and you take some measurements of Y, and get a set of data points X = (x1, x2, x3,...,xi). You want to know what the most probably estimator of Y is given your data points X. You want some probability density function, you don't know which one, to represent your error/probability of Y given the measurements X. Your only requirement is that it uses the arithmetic mean as the most probable value of Y given X (so mean of X = best guess of Y, but other than that, you have no restrictions and want a distribution). Given just these requirements, the only probability distribution you can derive is the normal distribution.
Similar thing for any other distribution. Most arise from mathematical problems: I have X data, I have some restraints/conditions, given the definition of a probability distribution, what do I end up with mathematically?
Now, to the second part:
>but for the life of me cant figure out how the make an equation that fits the distribution of dataFirst and foremost, all distributions are theoretical in nature and don't exist in real life. They just end up being good fits for what we want.
Generally, if you collect data, you pick a distribution which makes sense, given what you are measuring. Something not really taught but is intuitive to some degree, you usually you pick based on the principle of maximum entropy: which distribution maximizes entropy given my data?
In frequentist statistics, you usually frame the problem as: there's a hidden "generator" from a probability distribution that is spitting out data, I collected this X data, can I estimate the parameters of the distribution that is spitting out data?
