Oncological data applications and risk measures of the heavy-tailed Weibull flexible-G family

Fastel Chipepa; Mahmoud M. Abdelwahab; Wilbert Nkomo; Mustafa M. Hasaballah; Fastel Chipepa; Mahmoud M. Abdelwahab; Wilbert Nkomo; Mustafa M. Hasaballah

doi:10.3934/math.2026344

AIMS Mathematics

2026, Volume 11, Issue 3: 8382-8406. doi: 10.3934/math.2026344

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Oncological data applications and risk measures of the heavy-tailed Weibull flexible-G family

1.
Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
2.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3.
Department of Applied Statistics, Manicaland State University of Applied Sciences, P. Bag 7001, Stair Guthrie Road, Fernhill, Mutare, Zimbabwe
4.
Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt

Received: 13 January 2026 Revised: 16 February 2026 Accepted: 28 February 2026 Published: 30 March 2026
MSC : 62E10, 60E30

We introduce the heavy-tailed Weibull flexible-G (HT-WF-G) family of distributions and derive its fundamental properties, including quantile functions and moments. A maximum likelihood estimation procedure is developed for the parameter inference, with its finite-sample performance and asymptotic properties validated through rigorous Monte Carlo simulation studies. Furthermore, we formulate key actuarial risk metrics including the value at risk (VaR), tail value at risk (TVaR), tail variance (TV), and tail variance premium (TVP) within this flexible framework. The model's practical effectiveness is demonstrated through its application to oncology time-to-event data (lung cancer and acute myeloid leukemia). Empirical results consistently affirm the model's superiority over leading benchmark distributions, as evidenced by significant improvements in the goodness-of-fit criteria, thus establishing the HT-WF-G family as an effective tool for statistical modeling in heavy-tailed and complex survival settings.
- heavy-tailed-G,
- Weibull-flexible-G,
- estimation,
- Monte Carlo simulations,
- risk metrics,
- goodness-of-fit
Citation: Fastel Chipepa, Mahmoud M. Abdelwahab, Wilbert Nkomo, Mustafa M. Hasaballah. Oncological data applications and risk measures of the heavy-tailed Weibull flexible-G family[J]. AIMS Mathematics, 2026, 11(3): 8382-8406. doi: 10.3934/math.2026344

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Abstract

We introduce the heavy-tailed Weibull flexible-G (HT-WF-G) family of distributions and derive its fundamental properties, including quantile functions and moments. A maximum likelihood estimation procedure is developed for the parameter inference, with its finite-sample performance and asymptotic properties validated through rigorous Monte Carlo simulation studies. Furthermore, we formulate key actuarial risk metrics including the value at risk (VaR), tail value at risk (TVaR), tail variance (TV), and tail variance premium (TVP) within this flexible framework. The model's practical effectiveness is demonstrated through its application to oncology time-to-event data (lung cancer and acute myeloid leukemia). Empirical results consistently affirm the model's superiority over leading benchmark distributions, as evidenced by significant improvements in the goodness-of-fit criteria, thus establishing the HT-WF-G family as an effective tool for statistical modeling in heavy-tailed and complex survival settings.

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