A reduced distribution of the modified Weibull distribution and its applications to medical and engineering data

In this work, we suggest a reduced distribution with two parameters of the modified Weibull distribution to avoid some estimation difficulties. The hazard rate function of the reduced distribution exhibits decreasing, increasing or bathtub shape. The suggested reduced distribution can be applied to many problems of modelling lifetime data. Some statistical properties of the proposed distribution have been discussed. The maximum likelihood is employed to estimate the model parameters. The Fisher information matrix is derived and then applied to construct confidence intervals for parameters. A simulation is conducted to illustrate the performance of maximum likelihood estimation. Four sets of real data are tested to prove the proposed distribution advantages. According to the statistical criteria, the proposed distribution fits the tested data better than some well-known two-and three-parameter distributions.