We use four-year time series of precipitable water (PW) and zenith neutral delay (ZND) derived from a GPS network in Hawaii to show that the statistical distributions of these quantities are closely approximated by the lognormal distribution. The long term average and median values of precipitable water decline exponentially with height, or very nearly so. The arithmetic standard deviation of PW declines nearly linearly with height, whereas the geometric standard deviation increases nearly linearly (but relatively weakly). Our finding that PW has, to a good approximation, a lognormal distribution between sea level and 4 km elevation is confirmed by an analysis of radiosonde profiles. Lognormality is a common property of other meteorological quantities such as precipitation, aerosol optical and cloud distributions. This is the first time, as far as we know, that PW has also been shown to have a lognormal distribution.