Accurate distances to pulsars can be used for a variety of studies of the Galaxy and its electron content. However, most distance measures to pulsars have been derived from the absorption (or lack thereof) of pulsar emission by Galactic H I gas, which typically implies that only upper or lower limits on the pulsar distance are available. We present a critical analysis of all measured H I distance limits to pulsars and other neutron stars, and translate these limits into actual distance estimates through a likelihood analysis that simultaneously corrects for statistical biases. We also apply this analysis to parallax measurements of pulsars in order to obtain accurate distance estimates and find that the parallax and H I distance measurements are biased in different ways, because of differences in the sampled populations. Parallax measurements typically underestimate a pulsar's distance because of the limited distance to which this technique works and the consequential strong effect of the Galactic pulsar distribution (i.e., the original Lutz-Kelker bias), in H I distance limits, however, the luminosity bias dominates the Lutz-Kelker effect, leading to overestimated distances because the bright pulsars on which this technique is applicable are more likely to be nearby given their brightness.
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