The EGpz distribution have been proposed. A comprehensive study of the
mathematical properties of the proposed distribution have been provided. The
moments, quantiles, mode, mean residual lifetime, mean deviations and Rényi
entropy have been obtained. The density of EGpz distribution is Log-concave and
log-convex. In addition, the Gompertz distribution can have increasing FR only
but the EGpz distribution can have increasing FR and bathtub shaped FR for
various