Chapter 2: Exponential Distribution and the Poisson Process

Importance of the Exponential Distribution

An Excel spreadsheet demonstrating an arrival process where interarrivals are exponential with rate λ = 1. The graph shows that histogram approximates the exponential density f(t) = λ·exp(-λt) = exp(-t). There are statistical tests, (e.g., chi-square) to determine the validity of the exponential assumption. You can read my hand-written notes about this test here.

Exponential distribution calculations: This Excel file calculates the probabilities and expected value related to the exponential. It also plots the graph of the density function f(t) = α·exp(-αt). As mentioned above, there are statistical tests, (e.g., chi-square) to determine the validity of the exponential assumption.

Erlang distribution

Here is a Wikipedia article about the Erlang distribution. Note how the density changes when the parameters change.