Probability Distribution - Terminology

Terminology

As probability theory is used in quite diverse applications, terminology is not uniform and sometimes confusing. The following terms are used for non-cumulative probability distribution functions:

• Probability mass, Probability mass function, p.m.f.: for discrete random variables.
• Categorical distribution: for discrete random variables with a finite set of values.
• Probability density, Probability density function, p.d.f: Most often reserved for continuous random variables.

The following terms are somewhat ambiguous as they can refer to non-cumulative or cumulative distributions, depending on authors' preferences:

• Probability distribution function: Continuous or discrete, non-cumulative or cumulative.
• Probability function: Even more ambiguous, can mean any of the above, or anything else.

Finally,

• Probability distribution: Either the same as probability distribution function. Or understood as something more fundamental underlying an actual mass or density function.