Selecting the Family of Distribution

There are many different distributions that may fit into a specific simulation task. Though exponential, normal and Poisson distributions are the ones used most often, others such as gamma and Weibull distributions are useful and important as well.

Here is a list of commonly used distributions.

Binomial

Models the number of successes in n trials, when the trials are independent with common success probability, p.

Negative Binomial including the geometric distribution

Models the number of trials required to achieve k successes.

Poisson

Models the number of independent events that occur in a fixed amount of time or space.

Normal

Models the distribution of a process that can be thought of as the sum of a number of component processes.

Log-normal

Models the distribution of a process that can be thought of as the product of a number of component processes.

Exponential

Models the time between independent events, or a process time which is memoryless.

Gamma

An extremely flexible distribution used to model non-negative random variables.

Beta

An extremely flexible distribution used to model bounded random variables.

Erlang

Models processes that can be viewed as the sum of several exponentially distributed processes.

Weibull

Models the time-to-failure for components.

Discrete or Continuous Uniform

Models complete uncertainty, since all outcomes are equally likely.

Triangular

Models a process when only the minimum, most-likely, and maximum values of the distribution are known.

Empirical

Resamples from the actual data collected.