On a Flexible Three-Parameter Lifetime Model: Theoretical Properties and Real-Data Applications

Authors

  • Aafaq A. Rather Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune, India
  • Adil Rashid Postgraduate Department of Statistic, University of Kashmir, Srinagar, J&K, India
  • M. I. Khan Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, 42351, Kingdom of Saudi Arabia
  • Nazima Akhtar Postgraduate Department of Statistic, University of Kashmir, Srinagar, J&K, India
  • Zahoor Ahmad Postgraduate Department of Statistic, University of Kashmir, Srinagar, J&K, India

DOI:

https://doi.org/10.13052/jrss0974-8024.1925

Keywords:

Sujatha distribution, power series distribution, lifetime models, hazard rate, reliability analysis, maximum likelihood estimation, order statistics

Abstract

This paper introduces a new three-parameter lifetime model, called the Sujatha Power Series (SPS) distribution, motivated by the need for more flexible distributions in reliability and survival analysis. The model is constructed by compounding the Sujatha distribution with a family of power-series distributions, allowing it to accommodate various density and hazard rate shapes, including the important bathtub form. Key distributional properties are derived, and parameter estimation is performed using maximum likelihood methods. The practical performance of the SPS distribution is demonstrated through applications to two real lifetime datasets and comparisons with established competing models. The results indicate that the proposed model provides superior or comparable fits, highlighting its usefulness as an effective and flexible tool for modeling lifetime data in reliability and survival studies.

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Author Biographies

Aafaq A. Rather, Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune, India

Aafaq A. Rather is an Assistant Professor at the Symbiosis Statistical Institute, India. He has published more than 130 research papers in SCI, ESCI, Scopus-indexed, and other reputed international journals. His research interests include probability distributions, reliability analysis, survival analysis, and statistical modeling. Dr. Rather is actively involved in research supervision and has contributed significantly to the field of applied statistics through his academic and research activities.

Adil Rashid, Postgraduate Department of Statistic, University of Kashmir, Srinagar, J&K, India

Adil Rashid is a scholar in the field of Statistics who earned his PhD in Statistics in 2017. Over the years, he has contributed extensively to academic and research activities, with numerous research papers published in different areas of statistics and medical research. His work has reflected a strong interest in applied statistical methods and their role in scientific investigation.

Dr. Rashid has served as a lecturer in various colleges, where he has been actively involved in teaching, academic mentoring, and research guidance. Through his teaching career, he has gained recognition for his dedication toward students and his ability to simplify complex statistical concepts.

Presently, he is working as a Lecturer in Statistics at Government Degree College (GDC) Pulwama, where he continues to contribute to academics and research while encouraging students to engage in analytical and evidence based learning.

M. I. Khan, Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, 42351, Kingdom of Saudi Arabia

M. I. Khan received M.Sc. and Ph.D. from Aligarh Muslim University, India. Currently, he is working as an associate professor at the Department of Mathematics, Islamic University of Madinah, Kingdom of Saudi Arabia. His research has been focused in the area of mathematical statistics and ordered random variables.

Nazima Akhtar, Postgraduate Department of Statistic, University of Kashmir, Srinagar, J&K, India

Nazima Akhtar is a Lecturer in Statistics in Department of School Education, Jammu and Kashmir. She holds Phd degree in Statistics from the University of Kashmir. She has published work in international and national journals of repute. Her research interests include Distribution theory, and Estimation theory.

Zahoor Ahmad, Postgraduate Department of Statistic, University of Kashmir, Srinagar, J&K, India

Zahoor Ahmad is Lecturer of Statistics in Department of School Education, Jammu and Kashmir. He holds Phd degree in Statistics from the University of Kashmir and has been a gold medalist. He has published work in international and national journals of repute. His research interests include Distribution theory, Estimation theory and Bio-Statistics.

References

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Published

2026-07-02

How to Cite

Rather, A. A. ., Rashid, A. ., Khan, M. I. ., Akhtar, N. ., & Ahmad, Z. . (2026). On a Flexible Three-Parameter Lifetime Model: Theoretical Properties and Real-Data Applications. Journal of Reliability and Statistical Studies, 19(02), 347–386. https://doi.org/10.13052/jrss0974-8024.1925

Issue

2026: Vol 19 Iss 2

Section

Articles