  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 drop's dependence on absorber redshift.
