Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling

Şeyda Demirel Tatlı; Hasan Hüseyin Gül

doi:10.17798/bitlisfen.1780116

Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling

Abstract

Sampling methods are fundamental approaches that enhance the efficiency of scientific studies. However, to minimize ranking errors and obtain more accurate estimators, it is essential to develop alternative techniques to classical methods. The Median Ranked Set Sampling (MRSS) method stands out as a robust tool that minimizes ranking errors and enables more efficient evaluation of data. This method is particularly effective in improving the accuracy of sampling processes. On the other hand, the Unit-Gompertz (UG) distribution, with its flexible structure and parameters confined to the [0,1] interval, has emerged as a significant modeling option in fields such as health sciences, reliability theory, and actuarial studies. This study aims to analyze the performance of the MRSS method for the unknown parameters of the UG distribution and compare it with the Simple Random Sampling (SRS) method to develop more effective estimations. In addition to simulation results, a real-data application is also provided to demonstrate the practical usefulness of the proposed approach. The results demonstrated that MRSS provides more accurate and efficient estimates compared to SRS.

Keywords

Ethical Statement

The study is complied with research and publication ethics.

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Details

Primary Language

English

Subjects

Statistical Theory, Probability Theory, Theory of Sampling, Applied Statistics

Journal Section

Research Article

Authors

Şeyda Demirel Tatlı
0000-0002-8736-5162
Türkiye

Hasan Hüseyin Gül ^*
0000-0001-9905-8605
Türkiye

Publication Date

March 24, 2026

Submission Date

September 8, 2025

Acceptance Date

February 13, 2026

Published in Issue

Year 2026 Volume: 15 Number: 1

DOI

https://doi.org/10.17798/bitlisfen.1780116

IZ

https://izlik.org/JA85PK64WZ

Cite

RIS / Bibtex

APA

Demirel Tatlı, Ş., & Gül, H. H. (2026). Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 15(1), 123-136. https://doi.org/10.17798/bitlisfen.1780116

AMA

1.Demirel Tatlı Ş, Gül HH. Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2026;15(1):123-136. doi:10.17798/bitlisfen.1780116

Chicago

Demirel Tatlı, Şeyda, and Hasan Hüseyin Gül. 2026. “Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 15 (1): 123-36. https://doi.org/10.17798/bitlisfen.1780116.

EndNote

Demirel Tatlı Ş, Gül HH (March 1, 2026) Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 15 1 123–136.

IEEE

[1]Ş. Demirel Tatlı and H. H. Gül, “Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 15, no. 1, pp. 123–136, Mar. 2026, doi: 10.17798/bitlisfen.1780116.

ISNAD

Demirel Tatlı, Şeyda - Gül, Hasan Hüseyin. “Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 15/1 (March 1, 2026): 123-136. https://doi.org/10.17798/bitlisfen.1780116.

JAMA

1.Demirel Tatlı Ş, Gül HH. Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2026;15:123–136.

MLA

Demirel Tatlı, Şeyda, and Hasan Hüseyin Gül. “Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 15, no. 1, Mar. 2026, pp. 123-36, doi:10.17798/bitlisfen.1780116.

Vancouver

1.Şeyda Demirel Tatlı, Hasan Hüseyin Gül. Maximum Likelihood Estimation of The Unit Gompertz Distribution Using Median Ranked Set Sampling. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2026 Mar. 1;15(1):123-36. doi:10.17798/bitlisfen.1780116

Cited By

Estimation of the Half-Logistic Inverse Rayleigh Distribution Parameters via Ranked Set Sampling: Methods and Applications

Mathematics

https://doi.org/10.3390/math14081281