  In this paper, we propose some representations of a generalized linear birth
process called fractional Yule process (fYp). We also derive the probability
distributions of the random birth and sojourn times. The inter-birth time
distribution and the representations then yield algorithms on how to simulate
sample paths of the fYp. We also attempt to estimate the model parameters in
order for the fYp to be usable in practice. The estimation procedure is then
tested using simulated data as well. We also illustrate some major
characteristics of fYp which will be helpful for real applications.
