Parameter Estimation and Testing for the Doubly Geometric Process with Lognormal Distribution: Application to Bladder Cancer Patients’ Data

Mustafa Hilmi Pekalp, Gültaç Eroğlu İnan () and Halil Aydoğdu ()
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Mustafa Hilmi Pekalp: Department of Actuarial Sciences, Faculty of Applied Sciences, Ankara University, 50, Yıl Mah. Münzeviler Cad., Ankara, Turkey
Gültaç Eroğlu İnan: Department of Statistics, Faculty of Science, Ankara University, Dögol Cad. Tandoğan, Ankara, Turkey
Halil Aydoğdu: Department of Statistics, Faculty of Science, Ankara University, Dögol Cad. Tandoğan, Ankara, Turkey

Asia-Pacific Journal of Operational Research (APJOR), 2025, vol. 42, issue 02, 1-27

Abstract: The geometric process (GP) has been widely utilized as a stochastic monotone model in the fields of probability and statistics. However, its practical application is often limited by certain assumptions. To address this, [Wu (2018). Doubly geometric process and applications. Journal of the Operational Research Society, 69(1), 66–67] introduced the doubly geometric process (DGP) as an extension of the GP model, relaxing some of its assumptions. Due to its ability to overcome the limitations of the GP model, the DGP has gained significant popularity in recent times. This study focuses on the parameter estimation problem for the DGP when the distribution of the first interarrival time follows a lognormal distribution with parameters δ and τ. We employ the maximum likelihood method to obtain estimates for both the model parameters and the distribution parameters. Additionally, we investigate the asymptotic joint distribution and statistical properties such as asymptotic unbiasedness and consistency of the estimators. Furthermore, we propose a novel test procedure to distinguish between the GP and DGP models. To assess the performance of the estimators and the proposed test procedure, we conduct a simulation study involving various sample sizes and parameter values. Finally, we present an application of the developed methods in fitting data from bladder cancer patients.

Keywords: Parameter estimation; consistency; maximum likelihood; doubly geometric process; hypothesis testing (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0217595924500143

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