  Spectra of high redshift QSOs show deep Gunn-Peterson absorptions on the blue
sides of the \Lya emissions lines. They can be decomposed into components
called \Lya leaks, defined to be emissive regions in complementary to otherwise
zero-fluxed absorption gaps. Just like \Lya absorption forests at low
redshifts, \Lya leaks are both easy to find in observations and containing rich
sets of statistical properties that can be used to study the early evolution of
the IGM. Among all properties of a leak profile, we investigate its equivalent
width in this paper, since it is weakly affected by instrumental resolution and
noise. Using 10 Keck QSO spectra at $z\sim6$, we have measured the number
density distribution function $n(W,z)$, defined to be the number of leaks per
equivalent width $W$ and per redshift $z$, in the redshift range $5.4 - 6.0$.
These new observational statistics, in both the differential and cumulative
forms, fit well to hydro numerical simulations of uniform ionizing background
in the $\Lambda$CDM cosmology. In this model, Ly $\alpha$ leaks are mainly due
to low density voids. It supports the early studies that the IGM at $z\simeq6$
would still be in a highly ionized state with neutral hydrogen fraction $\simeq
10^{-4}$. Measurements of $n(W,z)$ at $z>6$ would be effective to probe the
reionization of the IGM.
