Abstarct: In this thesis, some ramifiction of Weibull distribution such as generalized modified Weibull distribution and beta generalized Weibull was introduced for modeling bathtub or upside-down bathtub (unimodal) shaped failure rates and according to these distributions, a new six parameter distribution called beta generalized modified Weibull distribution is introduced. The importance of these distributions lies in ability to model monotone as well as non-monotonic failure rates. These distributions also has a number of well-known distributions as sub-models. after introduce the beta generalized modified Weibull (BGMW) distribution, the cumulative distribution function (cdf) and the probability density function (pdf) have been expressed as mixture of the generalized modified Weibull cdfs and pdfs. We derived two infinite sum representations for its moments and the non-linear equations for maximum likelyhood estimators are presented. The distribution is found to be superior to the existing sub-models on being fitted a real data set.