# What is the difference between statistical distribution and probabilistic distribution?

What is the difference between statistical distribution and probabilistic distribution?

Are these terms used interchangeably? Are they same or different?

• Sometimes the terms mean the same thing (as in "standard statistical distributions") and sometimes statistical distribution stands for the empirical distribution of the sample, estimate of the probability distribution of the population behind the sample. Jul 2, 2020 at 7:05

Sometimes the meaning is the same, but sometimes statistical distribution have the connotation of a distribution family, as an example "the normal distribution $$\mathcal{N}(\mu, \sigma^2)$$" which means the family of all normal distributions with $$-\infty<\mu<\infty, \sigma^2>0$$.