Statistics and distributions How do you know if a distribution fits the data you are analyzing?
For example, if I had data that based on my assumption can be distributed geometrically, how can I check that this distribution fits my data and how can I be sure that any model of this type will fit my data?

There are lots of hypothesis test you can perform to your data to check if it fits a given distribution. Here you are a list:
Bayesian information criterion
Kolmogorov–Smirnov test
Cramér–von Mises criterion
Anderson–Darling test
Shapiro–Wilk test
Chi-squared test
Akaike information criterion
Hosmer–Lemeshow test
Kuiper's test
Kernelized Stein discrepancy
Zhang's ZK, ZC and ZA tests
Moran test
Density Based Empirical Likelihood Ratio tests
In this link it is explained a procedure to find the best distribution.
In particular, here you are a paper explaining an example of how to measure the goodness of fit of a geometric distribution.
