Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Computational Simulations of Similar Probabilistic Distributions to the Binomial and Poisson Distributions

Version 1 : Received: 29 December 2019 / Approved: 2 January 2020 / Online: 2 January 2020 (05:19:27 CET)

How to cite: Frometa-Castillo, T.; Pyakuryal, A.; Wals-Zurita, A.; Mesbahi, A. Computational Simulations of Similar Probabilistic Distributions to the Binomial and Poisson Distributions. Preprints 2020, 2020010014. https://doi.org/10.20944/preprints202001.0014.v1 Frometa-Castillo, T.; Pyakuryal, A.; Wals-Zurita, A.; Mesbahi, A. Computational Simulations of Similar Probabilistic Distributions to the Binomial and Poisson Distributions. Preprints 2020, 2020010014. https://doi.org/10.20944/preprints202001.0014.v1

## Abstract

This study has developed a Matlab application for simulating statistical models project (SMp) probabilistic distributions that are similar to binomial and Poisson, which were created by mathematical procedures. The simulated distributions are graphically compared with these legendary distributions. The application allows to obtain many probabilistic distributions, and shows the trend (τ ) for n trials with success probability p, i.e. the maximum probability as τ=np. While the Poisson distribution PD(x;µ) is a unique probabilistic distribution, where PD=0 in x=+∞, the application simulates many SMp(x;µ,Xmax) distributions, where µ is the Poisson parameter and value of x with generally the maximum probability, and Xmax is upper limit of x with SMp(x;µ,Xmax) ≥ 0 and limit of the stochastic region of the random discrete variable X. It is shown that by simulation via, one can get many and better probabilistic distributions than by mathematical one.

## Keywords

simulation; binomial distribution; poison distribution; stochastic process; modelling

## Subject

Computer Science and Mathematics, Probability and Statistics