poisson_uncertain

Aleatory uncertain discrete variable - Poisson

Topics

discrete_variables, aleatory_uncertain_variables

Specification

• Alias: None

• Arguments: INTEGER

• Default: no poisson uncertain variables

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Required		lambdas	The parameter for the Poisson distribution, the expected number of events in the time interval of interest
Optional		initial_point	Initial values for variables
Optional		descriptors	Labels for the variables

Description

The Poisson distribution is used to predict the number of discrete events that happen in a single time interval. The random events occur uniformly and independently. The expected number of occurences in a single time interval is $\lambda$ , which must be a positive real number. For example, if events occur on average 4 times per year and we are interested in the distribution of events over six months, $\lambda$ would be 2. However, if we were interested in the distribution of events occuring over 5 years, $\lambda$ would be 20.

The probability mass function for the poisson distribution is given by:

$$f(x)=\frac{{\lambda }^x{e}^{-\lambda }}{x!},$$

where

• $\lambda$ is the expected number of events occuring in a single time interval

• $x$ is the number of events that occur in this time period

• f(x) is the probability that $x$ events occur in this time period

Theory

When used with some methods such as design of experiments and multidimensional parameter studies, distribution bounds are inferred to be [0, $\mu +3\sigma$ ].

For some methods, including vector and centered parameter studies, an initial point is needed for the uncertain variables. When not given explicitly, these variables are initialized to their means.