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Dakota Reference Manual
Version 6.16
Explore and Predict with Confidence
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Aleatory uncertain discrete variable - Poisson
This keyword is related to the topics:
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 | ||
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 periodWhen 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.