B.2 Modeling with Discrete Distributions

There are a wide variety of discrete random variables that often occur in simulation modeling. Appendix F.1 summarizes the functions and characteristics some common discrete distributions. Table B.1 provides an overview of some modeling situations for common discrete distributions.

Table B.1: Common Modeling Situations for Discrete Distributions
Distribution Modeling Situations
Bernoulli(p) independent trials with success probability \(p\)
Binomial(n,p) sum of \(n\) Bernoulli trials with success probability \(p\)
Geometric(p) number of Bernoulli trials until the first success
Negative Binomial(r,p) number of Bernoulli trials until the \(r^{th}\) success
Discrete Uniform(a,b) equally likely outcomes over range (a, b)
Discrete Uniform \(v_1, \cdots, v_n\) equally likely over values \(v_i\)
Poisson(\(\lambda\)) counts of occurrences in an interval, area, or volume

By understanding the modeling situations that produce data, you can hypothesize the appropriate distribution for the distribution fitting process.