Summary: In this paper, we introduce a new useful continuous distribution called generalized modified inverse Weibull distribution. This distribution is a four-parameter extension of the modified inverse Weibull which generalizes some well-known distributions. Various statistical and probabilistic properties are derived such as \(r^{\text{th}}\) moment, moment generating function, Renyi and Shannon entropies and hazard rate function. We also discuss estimation of the parameters by maximum likelihood and provide the information matrix. The likelihood ratio order (which implies the hazard rate and usual stochastic orders) between smallest order statistics from two independent heterogeneous samples of this new family are discussed. Finally, a real numerical example is also considered for illustrative purposes.