  The probability density functions of proton, anti-proton, and net-proton
multiplicity distributions are constructed from the Beam Energy Scan results of
the STAR experiment using the Pearson curve method. The constructed
distributions of proton and anti-proton are compared with Poisson and Binomial
distributions. The net-proton probability distributions are compared with
Skellam distributions to study the O(4) criticality near the chiral crossover
transition. The $C_{6}/C_{2}$ results estimated from the obtained PDFs are
compared with Skellam and Binomial baselines for the Beam Energy Scan data. The
current study shows some signatures of O(4) criticality, which can be further
investigated by precision measurements of the cumulants and understanding the
contribution of non-critical fluctuations to them. This study also provides a
baseline for the higher-order cumulant measurement in the upcoming RHIC BES II
program and future LHC run.
