  Using cosmological hydrodynamic simulations of the LCDM model, we present a
comparison between the simulation sample and real data sample of HI and HeII
Ly\alpha transmitted flux in the absorption spectra of the QSO HE2347-4342. The
LCDM model is successful in simultaneously explaining the statistical features
of both HI and HeII Ly\alpha transmitted flux. It includes: 1.) the power
spectra of the transmitted flux of HI and HeII can be well fitted on all scales
> 0.28h^{-1} Mpc for H, and > 1.1h^{-1} Mpc for He; 2.) the Doppler parameters
of absorption features of HeII and HI are found to be turbulent-broadening; 3.)
the ratio of HeII to HI optical depths are substantially scattered, due to the
significant effect of noise. A large part of the \eta-scatter is due to the
noise in the HeII flux. However, the real data contain more low-\eta events
than simulation sample. This discrepancy may indicate that the mechanism
leading extra fluctuations upon the simulation data, such as a fluctuating UV
radiation background, is needed. Yet, models of these extra fluctuations should
satisfy the constraints: 1.) if the fluctuations are Gaussian, they should be
limited by the power spectra of observed HI and HeII flux; 2.) if the
fluctuations are non-Gaussian, they should be limited by the observed
non-Gaussian features of the HI and HeII flux.
