Ly{\alpha} Equivalent Width Distribution of Ly{\alpha} Emitting Galaxies
  at Redshift z $\sim$ 4.5
  Ly{\alpha} line EWs provide important clues to the physical nature of high
redshift LAEs. However, measuring the Ly{\alpha} EW distribution of high-z
narrowband selected LAEs can be hard because many sources do not have broadband
photometry. We investigate the possible biases in measuring the intrinsic
Ly{\alpha} EW distribution for a LAE sample at z $\sim$ 4.5 in the Extended
CDFS. Only weak Malmquist-type bias in both the intrinsic Ly{\alpha} luminosity
function and the Ly{\alpha} EW distribution were found. However, the observed
EW distribution is severely biased if one only considers LAEs with detections
in the continuum. Taking the broadband non-detections into account requires
fitting the distribution of the broadband-to-narrowband ratio, which then gives
a larger EW distribution scale length. Assuming an exponential form of the
intrinsic Ly{\alpha} EW distribution dN/dEW = N exp(-EW/W$_0$), we obtain W$_0$
= 167+/-44{\AA} (uncorrected for IGM absorption of Ly{\alpha}). We discuss the
likely range of IGM absorption effects in light of recent measurements of
Ly{\alpha} line profiles and velocity offsets. Our data are consistent with
Ly{\alpha} EW being independent of UV luminosity (i.e., we do not see evidence
for the "Ando" effect). Our simulations also imply that broad-band images
should be 0.5-1 magnitude deeper than narrowband images for an effective and
reasonably complete LAE survey. Comparing with consistent measurements at other
redshifts, we see a strong evolution in Ly{\alpha} EW distribution with
redshift which goes as a power-law form of W$_0$ $\prop$(1+z)$^${\xi}, with
{\xi} = 1.1$\pm$0.1 (0.6$\pm$0.1) if no IGM corrections are applied to the
Ly{\alpha} line; or {\xi} = 1.7$\pm$0.1 (1.2$\pm$0.1) after applying a maximal
IGM-absorption correction to Ly{\alpha} line) for an exponential (a gaussian)
EW distribution from z = 0.3 to 6.5.
