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New 3-parameter survival distributions from Manly’s transform

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  • Rose Baker

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.

Suggested Citation

  • Rose Baker, 2025. "New 3-parameter survival distributions from Manly’s transform," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(15), pages 4953-4964, August.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:15:p:4953-4964
    DOI: 10.1080/03610926.2024.2440004
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