The LR1 Lifetime Distribution: Properties, Nonmonotone Hazard, and Statistical Inference

The LR1 distribution links an exponential lifetime and a four-stage gamma lifetime through a single positive parameter $λ$. Their rates, $2λ$ and $λ/2$, have a fixed ratio, whereas the exponential mixing probability $λ^2/(1+λ^2)$ changes with the parameter. This restriction produces a hazard that de