Ly \alpha line equivalent widths ( EWs ) provide important clues to the physical nature of high redshift Lyman alpha emitters ( LAEs ) .
However , measuring the Ly \alpha EW distribution of high-z narrowband selected LAEs can be hard because many sources do not have well measured 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 Chandra Deep Field South ( ECDFS ) .
We show that our source selection procedures produce only weak Eddington type bias in both the intrinsic Ly \alpha luminosity function and the Ly \alpha EW distribution .
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 d N / d EW = N exp ^ { - EW / W _ { 0 } } , we obtain W _ { 0 } = 167 ^ { +44 } _ { -19 } Å ( uncorrected for IGM absorption of Ly \alpha , and \sigma _ { g } = 160 ^ { +43 } _ { -12 } Å for a gaussian EW distribution ) .
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 } \propto ( 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 .