New 3-parameter survival distributions from Manly’s transform

Baker, Rose

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.

• Journal Article Type: Article
• Acceptance Date: Dec 4, 2024
• Online Publication Date: Jan 6, 2025
• Deposit Date: Jan 10, 2025
• Publicly Available Date: Jan 10, 2025
• Journal: Communications in Statistics - Theory and Methods
• Print ISSN: 0361-0926
• Electronic ISSN: 1532-415X
• Publisher: Taylor and Francis
• Peer Reviewed: Peer Reviewed
• Pages: 1-12
• DOI: https://doi.org/10.1080/03610926.2024.2440004