Relationship Between the Cox, Lehmann, Weibull, and Accelerated Lifetime Models

Cox and Oakes (Citation1984) claimed that a model satisfies the accelerated lifetime (AL) model and the proportional hazards (PH) model iff it is Weibull. Doksum and Nabeya (Citation1984) constructed a family of analytic non Weibull survival functions that satisfies both the PH and AL models. We further study the relationship between the PH, AL, Lehmann, and Weibull models without the restriction of absolute continuity.