Generating new families of distributions using the exponential reliability method

In this paper, a new modifying method has been introduced by adding extra parameter to generate a new family of distributions that has more flexibility and better model fitting. A special case has been considered; two parameters Weibull distribution. All the main properties of the new modified Weibull are derived, including CDF, PDF, hazard and reliability functions. The maximum likelihood estimation method is used to estimate unknown parameters. The modified Weibull distribution has been applied on two lifetime data sets after analyzing them.