Ralph Vince - Portfolio Mathematics

ch02 JWBK035-Vince February 12, 2007 6:50 Char Count= 0

Probability Distributions 85

FIGURE 2.28 Cumulative probability functions for the Poisson Distribution

(L=4.5)

The Exponential Distribution

Related to the Poisson Distribution is a continuous distribution with a wide

utility called theExponential Distribution, sometimes also referred to as

theNegative Exponential Distribution. This distribution is used to model

interarrival times in queuing systems; service times on equipment; and sud-

den, unexpected failures such as equipment failures due to manufacturing

defects, light bulbs burning out, the time that it takes for a radioactive

particle to decay, and so on. (There is a very interesting relationship be-

tween the Exponential and the Poisson Distributions. The arrival of calls

to a queuing system follows a Poisson Distribution, with arrival rate L. The

interarrival distribution (the time between the arrivals) is Exponential with

parameter 1/L.)

The probability density function N′(X) for the Exponential Distribution

is given as:

N′(X)=A∗EXP(−A∗X) (2.47)

where: A=The single parametric input, equal to 1/L in the Poisson

Distribution. A must be greater than 0.

EXP( )=The exponential function.