birth process A simple birth process is a birth process with rates . It models a population in which each individual gives birth repeatedly and independently at rate . Udny Yule studied the processes, so they may be known as Yule processes. The number of births in time from a simple birth process of population is given by: In exact form, the number of births is the negative binomial distribution with parameters and . For the special case , this is the geometric distribution with success rate . The expectation of the process grows exponentially; specifically, if then . A simple birth process with immigration is a modification of this process with rates . This models a population with births by each population member in addition to a constant rate of immigration into the system. Notes References Markov processes Poisson point processes