The Log (t+1) Weibull Distribution: A New Flexible Model for Slow Peaking Survival Data
DOI:
https://doi.org/10.62933/fyf9f761Keywords:
Log-Weibull,, Gradually rising,, Sharp jump,, Nonlinear behavior,, Pancreatic cancer,Abstract
This paper aims to develop a new distribution, known as the Log-Weibull distribution, as a modification of the basic Weibull distribution by replacing the time variable t with the logarithmic variable Log (1+t). This aims to achieve a more accurate and realistic representation of survival data with nonlinear behavior. The statistical properties of the new distribution were analyzed and compared with the Weibull distribution in terms of density functions, survival, and hazard functions. Trade-off measures (AIC, AICc, BIC, HQ, SHWTZ) and the mean square error (MSE) criterion were also used to measure the goodness of fit. The results showed that the Log-Weibull distribution exhibits a smoother behavior of the probability density function, starting from zero at t=0 and gradually rising to a peak representing the most probable time of the event, unlike the Weibull, which may exhibit a sharp jump at the beginning. Furthermore, the proposed distribution offers high flexibility in representing multivariate survival data over time, leading to increased accuracy.
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Copyright (c) 2026 Bashar Khalid Ali, Sackineh Shamil Jasim (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensed under a Creative Commons Attribution 4.0 International License: https://creativecommons.org/licenses/by/4.0/
