Version 1
: Received: 23 October 2023 / Approved: 24 October 2023 / Online: 24 October 2023 (07:52:09 CEST)
How to cite:
Irshad, M.R.; Ahammed, M.; Maya, R. Monitoring Mean of INAR(1) Process with Discrete Mixture Exponential Innovations. Preprints2023, 2023101490. https://doi.org/10.20944/preprints202310.1490.v1
Irshad, M.R.; Ahammed, M.; Maya, R. Monitoring Mean of INAR(1) Process with Discrete Mixture Exponential Innovations. Preprints 2023, 2023101490. https://doi.org/10.20944/preprints202310.1490.v1
Irshad, M.R.; Ahammed, M.; Maya, R. Monitoring Mean of INAR(1) Process with Discrete Mixture Exponential Innovations. Preprints2023, 2023101490. https://doi.org/10.20944/preprints202310.1490.v1
APA Style
Irshad, M.R., Ahammed, M., & Maya, R. (2023). Monitoring Mean of INAR(1) Process with Discrete Mixture Exponential Innovations. Preprints. https://doi.org/10.20944/preprints202310.1490.v1
Chicago/Turabian Style
Irshad, M.R., Muhammed Ahammed and Radhakumari Maya. 2023 "Monitoring Mean of INAR(1) Process with Discrete Mixture Exponential Innovations" Preprints. https://doi.org/10.20944/preprints202310.1490.v1
Abstract
This paper presents a new discrete counterpart of the mixture exponential distribution by utilizing the survival discretization method. The moment-generating function and associated moment measures are discussed. The distribution’s hazard rate function can assume increasing or decreasing forms, making it adaptable for diverse fields requiring count data modelling. The paper explores four distinct parameter estimation methods and assesses their performance through Monte Carlo simulations. The applicability of this distribution extends to time series analysis, particularly within the framework of the
first-order integer-valued autoregressive process. Additionally, the paper explores quality control applications, addressing serial dependence challenges in count data encountered in production and market management. The performance of two distinct control charts, the cumulative sum chart and the exponentially weighted moving average chart, is evaluated for their effectiveness in detecting shifts in the process means under various models. A bivariate Markov chain approach is used to estimate the average run lengths of these charts, offering valuable insights for implementation. Design recommendations for achieving robustness in-control chart applications are provided. The effectiveness of the proposed models and charts is illustrated using a real data, demonstrating their practical superiority.
Computer Science and Mathematics, Probability and Statistics
Copyright:
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.
