A Monotone and Non-Monotone Hazard Rate Model: Its Application in Real Scenario

Abstract

In this article, alpha power new logarithmic transformation (APNLT) is proposed to get the new lifetime distributions using some baseline distribution in order to get flexible and superior distributions in terms of fitting to the real data. For the application point of view, we have considered exponential distribution as an appropriate baseline distribution which has constant hazard rate function and thus we have obtained alpha power new logarithmic transformed exponential (APNLTE) distribution. It has increasing, decreasing and upside-down bathtub shapes of failure rate function. Several statistical properties of APNLTE distribution have also been studied. A real dataset is taken to compare this new distribution with some existing distributions.

Keywords

APNLTE-distribution / hazard rate function / Renyi entropy / maximum likelihood estimator

Author Contributions

Pa.K.: Conceptualization, Methodology, Investigation; Pr.K.: Conceptualization, Methodology, Visualization, Writing-Original draft preparation; S.P.: Conceptualization, Methodology, Visualization, Investigation, Software; D.K.: Supervision, Validation, Writing—Reviewing and Editing. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

No new data were generated or analyzed during this study.

Acknowledgments

Authors are deeply indebted to the editor-in-chief and learned referees of this journal for their valuable suggestions to improve the quality, contents and presentation of the research manuscript.

Conflicts of Interest

The authors declare no conflicts of interest.

Use of AI and AI-Assisted Technologies

The authors declare that they did not use AI tools for data analysis, image generation, or text drafting in this study.

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