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Using cosmological hydrodynamic simulations of the LCDM model, we present acomparison between the simulation sample and real data sample of HI and HeIILy\alpha transmitted flux in the absorption spectra of the QSO HE2347-4342. TheLCDM model is successful in simultaneously explaining the statistical featuresof both HI and HeII Ly\alpha transmitted flux. It includes: 1.) the powerspectra 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 parametersof 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 thesignificant effect of noise. A large part of the \eta-scatter is due to thenoise in the HeII flux. However, the real data contain more low-\eta eventsthan simulation sample. This discrepancy may indicate that the mechanismleading extra fluctuations upon the simulation data, such as a fluctuating UVradiation background, is needed. Yet, models of these extra fluctuations shouldsatisfy the constraints: 1.) if the fluctuations are Gaussian, they should belimited by the power spectra of observed HI and HeII flux; 2.) if thefluctuations are non-Gaussian, they should be limited by the observednon-Gaussian features of the HI and HeII flux.Comment: 21 pages, 7 figs, ApJ in pres

A Unified Fitting of Hiand HeiiLyα Transmitted Flux of QSO HE 2347−4342 with ΛCDM Hydrodynamic Simulations