When we want to fit your data with some parametric models, there are three categories that
we usually consider first:
The most significant character is its memoryless property. For example, if the bus arriving time is following exponential distribution, then your expected wait time would be the same as the average time between buses, no matter what time you arrive.
Statistically it means the number of successes in independent Bernoulli trials. Usually normal distribution would be a good approximation to Binomial when number of trials is large (~ 100 is large enough).
According to the Central Limit Theory, many distributions would eventually come to Gaussian distribution. So, if you are not sure about which distribution to select, try Gaussian first.
Here is the family tree of parametric distributions.
So the principles to choose a paramatric model are:
- know your situation
- know your data