A New Hjorth Distribution in Its Discrete Version

Hanan Haj Ahmad () and Ahmed Elshahhat
Additional contact information
Hanan Haj Ahmad: Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia
Ahmed Elshahhat: Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Mathematics, 2025, vol. 13, issue 5, 1-25

Abstract: The Hjorth distribution is more flexible in modeling various hazard rate shapes, including increasing, decreasing, and bathtub shapes. This makes it highly useful in reliability analysis and survival studies, where different failure rate behaviors must be captured effectively. In some practical experiments, the observed data may appear to be continuous, but their intrinsic discreteness requires the development of specialized techniques for constructing discrete counterparts to continuous distributions. This study extends this methodology by discretizing the Hjorth distribution using the survival function approach. The proposed discrete Hjorth distribution preserves the essential statistical characteristics of its continuous counterpart, such as percentiles and quantiles, making it a valuable tool for modeling lifetime data. The complexity of the transformation requires numerical techniques to ensure accurate estimations and analysis. A key feature of this study is the incorporation of Type-II censored samples. We also derive key statistical properties, including the quantile function and order statistics, and then employ maximum likelihood and Bayesian inference methods. A comparative analysis of these estimation techniques is conducted through simulation studies. Furthermore, the proposed model is validated using two real-world datasets, including electronic device failure times and ball-bearing failure analysis, by applying goodness-of-fit tests against alternative discrete models. The findings emphasize the versatility and applicability of the discrete Hjorth distribution in reliability studies, engineering, and survival analysis, offering a robust framework for modeling discrete data in practical scenarios. To our knowledge, no prior research has explored the use of censored data in analyzing discrete Hjorth-distributed data. This study fills this gap, providing new insights into discrete reliability modeling and broadening the application of the Hjorth distribution in real-world scenarios.

Keywords: discrete Hjorth; likelihood and Bayesian; survival analysis; censoring; order statistics; simulation; real-world applications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/5/875/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/5/875/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:5:p:875-:d:1606376

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().