New 3-parameter survival distributions from Manly’s transform

Rose Baker

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 15, 4953-4964

Abstract: Two new 3-parameter distributions that generalize the Weibull distribution are introduced. They fit a range of datasets comparably to the generalized gamma and exponentiated Weibull distributions, allowing increasing hazard, decreasing hazard, and bathtub and inverted bathtub hazards. The probability density function can be unimodal, J-shaped, or U-shaped. The survival function is given in closed form, and random numbers can be readily generated. Moments can be evaluated as integrals. For decreasing hazard distributions one distribution can also be a non mixture cure model, a promotion-time model, where the promotion time follows an exponentiated exponential distribution. The second, related distribution does not give a cure model.

Date: 2025
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DOI: 10.1080/03610926.2024.2440004

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