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    Author(s)

    Elhadji Ousseynouu Accrachi, PhD. Cherif Ahmat Tidiane Aidara — Academia (Universities, Colleges and other higher learning entities) (Université Gaston Berger), PhD. Ali Dabye — Academia (Universities, Colleges and other higher learning entities) (Université Gaston Berger)
    Category: Mathematics
    DOI: 10.52737/18291163-2019.11.5-1-13
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      On Parameter Estimation by Aggregated Poisson Observations

      Elhadji Ousseynouu Accrachi, PhD. Cherif Ahmat Tidiane Aidara — Academia (Universities, Colleges and other higher learning entities) (Université Gaston Berger), PhD. Ali Dabye — Academia (Universities, Colleges and other higher learning entities) (Université Gaston Berger)
      This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

      Submitted: 2024-12-10; Published: 2022-09-15
      © 2025 by author(s) and The Gufo Inc.
      CC BY-NC 4.0 This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

      Abstract

      We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.

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