  Using the Monte Carlo data at 7 TeV collected by the ATLAS collaboration
(PYTHIA 6), we examine the necessity of applying the three-negative binomial
distribution (T-NBD). By making use of the T-NBD formulation, we analyze the
multiplicity distribution (MD) and the Bose-Einstein correlation (BEC) at the
Large Hadron Collider (LHC). In the T-NBD framework, the BEC is expressed by
two degrees of coherence $\lambda_1$ and $\lambda_2$ and two kinds of exchange
functions $E_1^2$ and $E_2^2$ that act over interaction ranges $R_1$ and $R_2$,
respectively. Using the calculated $\lambda_1$ and $\lambda_2$ based on the
T-NBD, along with free $\lambda_1$ and $\lambda_2$, we analyze the BEC data at
0.9 and 7 TeV. The estimated parameters $R_1$ and $R_2$ are almost coincident
and seem to be consistent with $pp$ collisions. We also present an enlarged
Koba-Nielsen-Olesen (KNO) scaling function based on the T-NBD, and apply it to
KNO scaling at LHC energies. The enlarged scaling function describes the
observed violation of the KNO scaling.
