A New Inverted U-Shape Hazard Function

The hazard function describes the unobserved rate at which failures occur. In this paper, we present a new inverted U-shape hazard function, developed for risk-events related to human activities. This hazard shape has received less attention in the literature relative to monotone hazard functions, likely due to the mathematical complexity of their regression models. We present a new survivor function, based on a logarithm transformation, and time displacement of Weibull's survivor function, that has an inverted U-shape hazard function similar to the log-logistic one. The advantage of this hazard function relative to the Weibull, and log-logistic hazard functions is in its unique curvature, which may fit better in some cases. We use simulation studies to present the new distribution characteristics in comparison to the Weibull, and the log-logistic distributions.