In order to carry out a systematic and thorough measurement of the HI Gunn-Peterson effect at high redshift, a quantitatively testable and repeatable procedure, in particular, a robust statistical weighting technique, is developed. It is applied to an echelle spectrum of resolution 15 km s$^{-1}$ of PKS 1937-101 with z=3.787. A weighted intensity distribution which is derived overwhelmingly from pixels close to the continuum level in the Ly alpha forest region is constructed by the evaluation of how closely correlated each pixel is with its neighboring pixels. The merit of the distribution is its stronger and narrower peak compared to the unweighted, as well as its smaller dependence on uncertainty of strong absorption lines and noise spikes. By comparison to the weighted intensity distribution of synthetic Ly alpha forest spectrum with various chosen diffuse HI opacities, a chi square fit is performed. In addition to a weak line population with power law N_H distribution $beta =1.7$ extrapolated down to 10$^{12}$ cm$^{-2}$, a best chi square fit requires a GP opacity of $0.115 pm 0.025$ at average z=3.4 with estimation of the contribution from the variance of $beta$. Although no evidence of more than 1-2% error is seen in the continuum extrapolation, the possible systematic overestimation due to the slope can be as high as the level of the $chi^2$ fit, which is investigated by splitting the Lya forest region into subsamples to check the continuum drops dependence on absorber redshift.
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