A lifetime distribution with an upside-down bathtub-shaped hazard function

A three-parameter lifetime distribution with increasing, decreasing, bathtub, and upside down bathtub shaped failure rates is introduced. The new model includes the Weibull distribution as a special case. A motivation is given using a competing risks interpretation when restricting its parametric space. Various statistical properties, and reliability aspects are explored, and the estimation of parameters is studied using the standard maximum likelihood procedures. Applications of the model to real data are also included.