Application - [A11]

14-11-2022 210 words One minute

Contents

Question

Consider a general scheme ad the simulation of previous homework and simulate the distribution of p = SUM(xi) , where xi are Bernoulli(lambda/n), with success probability lambda /n, where lambda is a user constant (“arrival rate”). Also plot the distribution of the “interarrival times”.

Application

The application simulates a Poisson process, a stochastic model for the occurrence of events over time. It generates multiple samples, each consisting of a sequence of Bernoulli trials. The success probability in each trial is determined by the user-specified arrival rate ($\lambda$). The sum of these trials (p) is calculated for each sample, representing the arrival value. Moreover the interarrival times are calculated as the difference between the arrival times of two consecutive samples. Both the arrival values and the interarrival times are then plotted as histograms, that can be seen in the following images:

../images/bernoulli.png — Bernoulli distribution

../images/interarrivals.png — Interarrivals distribution

Library

For this application I used a self-developed library, the code for it can be found on the same Github repository used for the applications. The whole library can also be downloaded as a ZIP file from the Releases section.

Source Code

The application source code can be found on Github and the whole project folder is saved as a ZIP file in this Release