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Ly{\alpha} line EWs provide important clues to the physical nature of highredshift LAEs. However, measuring the Ly{\alpha} EW distribution of high-znarrowband selected LAEs can be hard because many sources do not have broadbandphotometry. We investigate the possible biases in measuring the intrinsicLy{\alpha} EW distribution for a LAE sample at z $\sim$ 4.5 in the ExtendedCDFS. Only weak Malmquist-type bias in both the intrinsic Ly{\alpha} luminosityfunction and the Ly{\alpha} EW distribution were found. However, the observedEW distribution is severely biased if one only considers LAEs with detectionsin the continuum. Taking the broadband non-detections into account requiresfitting the distribution of the broadband-to-narrowband ratio, which then givesa larger EW distribution scale length. Assuming an exponential form of theintrinsic 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 thelikely range of IGM absorption effects in light of recent measurements ofLy{\alpha} line profiles and velocity offsets. Our data are consistent withLy{\alpha} EW being independent of UV luminosity (i.e., we do not see evidencefor the "Ando" effect). Our simulations also imply that broad-band imagesshould be 0.5-1 magnitude deeper than narrowband images for an effective andreasonably complete LAE survey. Comparing with consistent measurements at otherredshifts, we see a strong evolution in Ly{\alpha} EW distribution withredshift which goes as a power-law form of W$_0$ $\prop$(1+z)$^${\xi}, with{\xi} = 1.1$\pm$0.1 (0.6$\pm$0.1) if no IGM corrections are applied to theLy{\alpha} line; or {\xi} = 1.7$\pm$0.1 (1.2$\pm$0.1) after applying a maximalIGM-absorption correction to Ly{\alpha} line) for an exponential (a gaussian)EW distribution from z = 0.3 to 6.5.

Ly{\alpha} Equivalent Width Distribution of Ly{\alpha} Emitting Galaxies at Redshift z $\sim$ 4.5