Finding an appropriate distribution

Thinking about how a measurement is made sometimes suggests that the variable's distribution should belong to a family of standard distributions, such as a uniform, binomial, geometric or negative binomial distribution.

This reasoning may require some assumptions about the process underlying the variable.

Unfortunately, this usually only leads to a family of standard distributions with one or more parameters whose values are unknown, such as the probability of success \(\pi\) in a series of Bernoulli trials.

How can we find the value of any such unknown parameter?