Many different distributions have a power-law tail decay, such as the Internet degree distribution, the species genera distribution, the terror attack distribution and more. Many of these distributions were described by a preferential attachment model that is also know as the Yule model. However, this model cannot explain the whole distribution, but only the power-law tail. The beginning of the distribution that does not follow the power law tail cannot be explained. In addition, the preferential attachment model ignores the very likely event of the death of a link. We developed a new model that includes the option of a death event, and solved it analytically. With the addition of the death event, we are able to explain the entire distribution of many processes.