Optimizing analgesic pain relief time analysis through Bayesian and non-Bayesian approaches to new right truncated Fréchet-inverted Weibull distribution

Nora Nader; Dina A. Ramadan; Hanan Haj Ahmad; M. A. El-Damcese; B. S. El-Desouky; Nora Nader; Dina A. Ramadan; Hanan Haj Ahmad; M. A. El-Damcese; B. S. El-Desouky

doi:10.3934/math.20231598

AIMS Mathematics

2023, Volume 8, Issue 12: 31217-31245. doi: 10.3934/math.20231598

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Optimizing analgesic pain relief time analysis through Bayesian and non-Bayesian approaches to new right truncated Fréchet-inverted Weibull distribution

1.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt
2.
Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf 31982, Al Ahsa, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Tanta University, Tanta 663211, Egypt

Received: 11 September 2023 Revised: 05 November 2023 Accepted: 09 November 2023 Published: 23 November 2023
MSC : 62N05, 62N02, 62N01, 62H12, 62F15, 62F10, 62F40

This research introduces a novel right-truncated distribution, termed the right truncated Fréchet-inverted Weibull distribution, and elucidates its mathematical properties including density, cumulative, survival and hazard functions. Various statistical attributes such as moments, quantile, mode and moment-generating functions are explored. These properties indicate the efficiency in modeling pain relief time for patients and the number of recoveries of Leukemia patients. Furthermore, estimation techniques, including maximum likelihood and Bayesian methods, are applied to progressive type-Ⅱ right-censored samples to derive parameter estimation of the proposed distribution. Asymptotic properties are employed to approximate confidence intervals for both reliability and hazard functions. Bayesian estimates are refined using both symmetric and asymmetric loss functions. The suitability of the proposed estimation methodologies is validated through simulation studies. The theoretical framework is applied to two real-world lifetime data sets, thereby substantiating their practical utility in medical areas.
- Weibull distribution,
- Fréchet distribution,
- maximum likelihood estimators,
- progressive type-Ⅱ censoring,
- Bayes estimation,
- simulation,
- modeling
Citation: Nora Nader, Dina A. Ramadan, Hanan Haj Ahmad, M. A. El-Damcese, B. S. El-Desouky. Optimizing analgesic pain relief time analysis through Bayesian and non-Bayesian approaches to new right truncated Fréchet-inverted Weibull distribution[J]. AIMS Mathematics, 2023, 8(12): 31217-31245. doi: 10.3934/math.20231598

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Abstract

This research introduces a novel right-truncated distribution, termed the right truncated Fréchet-inverted Weibull distribution, and elucidates its mathematical properties including density, cumulative, survival and hazard functions. Various statistical attributes such as moments, quantile, mode and moment-generating functions are explored. These properties indicate the efficiency in modeling pain relief time for patients and the number of recoveries of Leukemia patients. Furthermore, estimation techniques, including maximum likelihood and Bayesian methods, are applied to progressive type-Ⅱ right-censored samples to derive parameter estimation of the proposed distribution. Asymptotic properties are employed to approximate confidence intervals for both reliability and hazard functions. Bayesian estimates are refined using both symmetric and asymmetric loss functions. The suitability of the proposed estimation methodologies is validated through simulation studies. The theoretical framework is applied to two real-world lifetime data sets, thereby substantiating their practical utility in medical areas.

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