What are some examples of distribution function?

Answer 1

I will assume that you are asking about probability distribution functions. There are two types: discrete and continuous. Some might argue that a third type exists, which is a mix of discrete and continuous distributions.

When representing discrete random variables, the probability distribution is probability mass function or "pmf." For continuous distributions, the theoretical distribution is the probability density function or "pdf."

Some textbooks will call pmf's as discrete probability distributions.

Common pmf's are binomial, multinomial, uniform discrete and Poisson.

Common pdf's are the uniform, normal, log-normal, and exponential.

Two common pdf's used in sample size, hypothesis testing and confidence intervals are the "t distribution" and the chi-square. Finally, the F distribution is used in more advanced hypothesis testing and regression.