Abstract
The widely known generators of Poisson random variables are associated with different modifications of the algorithm based on the convergence in probability of a sequence of uniform random variables to the created stochastic number. However, in some situations, this approach yields different discrete Poisson probability distributions and skipping in the generated numbers. This article offers a new approach for creating Poisson random variables based on the complete twister generator of uniform random variables, using cumulative frequency technology. The simulation results confirm that probabilistic and frequency distributions of the obtained stochastic numbers completely coincide with the theoretical Poisson distribution. Moreover, combining this new approach with the tuning algorithm of basic twister generation allows for a significant increase in length of the created sequences without using additional RAM of the computer.
Highlights
IntroductionPoisson distribution simulates a random variable that represents the number of events that occurred over a fixed time
Using generators of Poisson random variables realizes a stochastic process of creating integer random numbers η ∈ H having the following probability distribution with respect to the real parameter α [1,2]: αη −α P(η, α) = e, (1) η!where η takes any integer values such as 0, 1, 2, . . . , ∞.The Poisson model usually describes a scheme of rare events: under certain assumptions about the nature of a process with random events, the number of elements observed over a fixed time interval or in a fixed region of space is often a subject of Poisson distribution
Is class nsDeonYuliCPoissonTwist32D, in which the random variables are created in accordance with Poisson distribution (13)
Summary
Poisson distribution simulates a random variable that represents the number of events that occurred over a fixed time. These events happened with some fixed average intensity and independently of each other. Poisson distribution is discrete, which is one of the important limiting cases of a binomial distribution. It gives a good approximation of a binomial distribution for both small and large values. In this case, Poisson distribution is intensively used in quality control cards, queuing theory, telecommunications, etc
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
