Proportional Autoregressive Quasi-Lindley Half-Logistic Unit Process with Application in Modeling Crime Dynamics

Stojanović, Vladica S.; Bakouch, Hassan S.; Stojičić, Snežana; Alghmadi, Shuhrah

doi:10.3390/sym18091482

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Proportional Autoregressive Quasi-Lindley Half-Logistic Unit Process with Application in Modeling Crime Dynamics

¹

Department of Informatics & Computer Sciences, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia

²

Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

³

Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt

⁴

Department of Forensic Engineering, University of Criminal Investigation and Police Studies, 11000 Belgrade, Serbia

⁵

Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11564, Saudi Arabia

^*

Author to whom correspondence should be addressed.

Symmetry 2026, 18(9), 1482; https://doi.org/10.3390/sym18091482

Submission received: 9 August 2026 / Revised: 31 August 2026 / Accepted: 1 September 2026 / Published: 3 September 2026

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, 5th Edition)

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Abstract

The manuscript proposes a novel bounded proportional autoregressive (PAR) process based on the quasi-Lindley half-logistic unit (QHU) distribution, termed the QHU-PAR(1) process. Fundamental probabilistic properties of the process are established, including its Markov structure, moments, and stationarity conditions. A pseudo-innovation-based parameter estimation procedure is performed, demonstrating strong consistency and asymptotic normality of the resulting estimators. A Monte Carlo study is also conducted, showing satisfactory performance of the proposed estimators on finite samples, while the practical utility of the model is illustrated through the analysis of normalized crime-related time series. Comparative results show that the proposed QHU-PAR(1) process outperforms some competing specifications, highlighting its flexibility and efficiency for modeling bounded and asymmetric stochastic phenomena.

Keywords: bounded time series; autoregressive process; asymmetric distribution; stationarity; asymptotic inference; Monte Carlo simulation; crime data analysis

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MDPI and ACS Style

Stojanović, V.S.; Bakouch, H.S.; Stojičić, S.; Alghmadi, S. Proportional Autoregressive Quasi-Lindley Half-Logistic Unit Process with Application in Modeling Crime Dynamics. Symmetry 2026, 18, 1482. https://doi.org/10.3390/sym18091482

AMA Style

Stojanović VS, Bakouch HS, Stojičić S, Alghmadi S. Proportional Autoregressive Quasi-Lindley Half-Logistic Unit Process with Application in Modeling Crime Dynamics. Symmetry. 2026; 18(9):1482. https://doi.org/10.3390/sym18091482

Chicago/Turabian Style

Stojanović, Vladica S., Hassan S. Bakouch, Snežana Stojičić, and Shuhrah Alghmadi. 2026. "Proportional Autoregressive Quasi-Lindley Half-Logistic Unit Process with Application in Modeling Crime Dynamics" Symmetry 18, no. 9: 1482. https://doi.org/10.3390/sym18091482

APA Style

Stojanović, V. S., Bakouch, H. S., Stojičić, S., & Alghmadi, S. (2026). Proportional Autoregressive Quasi-Lindley Half-Logistic Unit Process with Application in Modeling Crime Dynamics. Symmetry, 18(9), 1482. https://doi.org/10.3390/sym18091482

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Proportional Autoregressive Quasi-Lindley Half-Logistic Unit Process with Application in Modeling Crime Dynamics

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