Dakota Reference Manual  Version 6.15
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poisson_uncertain


Aleatory uncertain discrete variable - Poisson

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): 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.