  In 1990, Jakeman (see \cite{jakeman1990statistics}) defined the binomial
process as a special case of the classical birth-death process, where the
probability of birth is proportional to the difference between a fixed number
and the number of individuals present. Later, a fractional generalization of
the binomial process was studied by Cahoy and Polito (2012) (see
\cite{cahoy2012fractional}) and called it as fractional binomial process (FBP).
In this paper, we study second-order properties of the FBP and the long-range
behavior of the FBP and its noise process. We also estimate the parameters of
the FBP using the method of moments procedure. Finally, we present the
simulated sample paths and its algorithm for the FBP.
