Dakota Reference Manual: poisson_uncertain

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poisson_uncertain

Aleatory uncertain discrete variable - Poisson

## Topics

This keyword is related to the topics:

- discrete_variables
- aleatory_uncertain_variables

## 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 , 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, would be 2. However, if we were interested in the distribution of events occuring over 5 years, would be 20.

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

where

- 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, ].

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.