Statistical Inference for Multi-sample of Geometric Processes with Lognormal Distribution

Ömer Altındağ; Halil Aydoğdu

doi:10.31801/cfsuasmas.1765197

Statistical Inference for Multi-sample of Geometric Processes with Lognormal Distribution

Abstract

The geometric process is an important counting process model that serves as an alternative to non-homogeneous Poisson process models. It is widely used in reliability analysis, particularly in the modeling of repairable systems, due to its monotonic behaviour. Accurate statistical inference for a geometric process is essential for appropriate data modeling. While extensive research has addressed inference in the single-sample case, real-world data are often collected from multiple sources, leading to multi-sample datasets. This introduces new challenges for statistical inference. In this study, we investigate the inference problem for a geometric process based on multi-sample data, under the assumption that the inter-arrival times of each process follow a lognormal distribution and that the samples are homogeneous. Maximum likelihood estimators of the model parameters are obtained, and their asymptotic characteristics are established. The Expectation-Maximization algorithm is adopted to compute the maximum likelihood estimators in case of censored observations. Additionally, we propose test statistics for assessing the homogeneity of the samples and for detecting the presence of a trend in the data. A simulation analysis is undertaken to evaluate and compare the maximum likelihood estimators against their non-parametric counterparts. Finally, the proposed inferential procedures are illustrated using a real dataset comprising failure data from two machining centers.

Keywords

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Details

Primary Language

English

Subjects

Statistical Analysis, Stochastic Analysis and Modelling

Journal Section

Research Article

Authors

Ömer Altındağ ^*
0000-0002-7035-9612
Türkiye

Halil Aydoğdu
0000-0001-5337-5277
Türkiye

Publication Date

September 26, 2026

Submission Date

August 14, 2025

Acceptance Date

March 12, 2026

Published in Issue

Year 2026 Volume: 75 Number: 3

DOI

https://doi.org/10.31801/cfsuasmas.1765197

IZ

https://izlik.org/JA66DY59NJ

Cite

RIS / Bibtex

APA

Altındağ, Ö., & Aydoğdu, H. (2026). Statistical Inference for Multi-sample of Geometric Processes with Lognormal Distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 75(3), 507-537. https://doi.org/10.31801/cfsuasmas.1765197

AMA

1.Altındağ Ö, Aydoğdu H. Statistical Inference for Multi-sample of Geometric Processes with Lognormal Distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75(3):507-537. doi:10.31801/cfsuasmas.1765197

Chicago

Altındağ, Ömer, and Halil Aydoğdu. 2026. “Statistical Inference for Multi-Sample of Geometric Processes With Lognormal Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 (3): 507-37. https://doi.org/10.31801/cfsuasmas.1765197.

EndNote

Altındağ Ö, Aydoğdu H (September 1, 2026) Statistical Inference for Multi-sample of Geometric Processes with Lognormal Distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 3 507–537.

IEEE

[1]Ö. Altındağ and H. Aydoğdu, “Statistical Inference for Multi-sample of Geometric Processes with Lognormal Distribution”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 75, no. 3, pp. 507–537, Sept. 2026, doi: 10.31801/cfsuasmas.1765197.

ISNAD

Altındağ, Ömer - Aydoğdu, Halil. “Statistical Inference for Multi-Sample of Geometric Processes With Lognormal Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75/3 (September 1, 2026): 507-537. https://doi.org/10.31801/cfsuasmas.1765197.

JAMA

1.Altındağ Ö, Aydoğdu H. Statistical Inference for Multi-sample of Geometric Processes with Lognormal Distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75:507–537.

MLA

Altındağ, Ömer, and Halil Aydoğdu. “Statistical Inference for Multi-Sample of Geometric Processes With Lognormal Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 75, no. 3, Sept. 2026, pp. 507-3, doi:10.31801/cfsuasmas.1765197.

Vancouver

1.Ömer Altındağ, Halil Aydoğdu. Statistical Inference for Multi-sample of Geometric Processes with Lognormal Distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026 Sep. 1;75(3):507-3. doi:10.31801/cfsuasmas.1765197