Predicting intensity function of nonhomogeneous Poisson process

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Yarmohammadi Masoud; Afshar Ada; Mahmoudvand Rahim; Nasiri Parviz

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Journal Paper

Paper Information

Journal: JOURNAL OF STATISTICAL MODELLING: THEORY AND APPLICATIONS Year:2022 | Volume:3 | Issue:2 Page(s): 39-50

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Title

Predicting intensity function of nonhomogeneous Poisson process

Author(s)

Yarmohammadi Masoud | Afshar Ada | Mahmoudvand Rahim | Nasiri Parviz | Issue Writer Certificate

Keywords

Hypothesis testing

Intensity Function

Nonhomogeneous Poisson process

Poisson process

Abstract

The Poisson process/fa?page=1&sort=1&ftyp=all&fgrp=all&fyrs=all" target="_blank">Nonhomogeneous Poisson process is commonly utilized to model the occurrence of events over time‎. ‎The identification of Poisson process/fa?page=1&sort=1&ftyp=all&fgrp=all&fyrs=all" target="_blank">Nonhomogeneous Poisson process relies on the Intensity Function‎, ‎which can be difficult to determine‎. ‎A straightforward approach is to set the Intensity Function to a constant value‎, ‎resulting in a homogeneous Poisson process‎. ‎However‎, ‎it is crucial to assess the homogeneity of the Intensity Function through an appropriate test beforehand‎. ‎Failure to confirm homogeneity leads to an infinite-dimensional problem that cannot be comprehensively resolved‎. ‎In this study‎, ‎we analyzed data on the number of passengers using the Tehran metro‎. ‎Our homogeneity test showed a nonhomogeneous arrival rate of passengers‎, ‎prompting us to explore different functions to estimate the Intensity Function‎. ‎We considered four functions and used a piecewise function to determine the best Intensity Function‎. ‎Our findings showed significant differences between the two models‎, ‎highlighting the effectiveness of the piecewise function model in predicting the number of metro passengers.

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