Chen (2000) proposed a big family of distributions which is suitable for life model since its hazard rate function has a bathtub shape. Unfortunately, the proposed estimate for the parameter is not an exact MLE. In this thesis, we propose the minimum Hellinger distance estimate (MHDE) for the parameters involved in the family. This MHDE has good properties; it possesses not only the first order efficiency, but also robustness. When the data is contaminated, robust estimate is an appropriate choice. Some numerical simulations have been carried out both for the case of maximum likelihood like estimate and MHDE. Some improved estimate has been proposed. Finally, some extension of the Chen’s model has also been made.