On the basis of the narrowband approximation the joint and marginal probability distribution functions (pdf) of local wave heights and periods of ocean surface waves have been derived and have been taken approximately as those of the crest-to-trough wave heights and zero upcrossing periods. Various correction schemes have been proposed to these pdf's in order to apply them to broadband waves. This paper is devoted to taking a close look at these correction schemes. The relationship between the distributions of the local and the discrete wave heights and periods is derived at first. This derivation provides a precise interpretation to the improvements due to Stansell et al. (2004) and Zheng et al. (2004). The resultant relationship is different from the one deduced by Kitano and Mase (1998), on which their improved wave height distribution rests. The unique analysis of Kitano and Mase (1998) leading to this relationship is inspected and their omission is found. The crest-to-trough wave height distribution proposed by Tayfun (1981) is also examined and found to be reasonable only when the spectral bandwidth is infinitesimal. The wind wave data measured in Bohai China in 1997 is analyzed here. The sensitivities of the measured (as opposed to actual) distributions to smoothing timescale and to sampling rate are explored and comparisons of various theoretical pdf's with the measured distributions are made. It is found that (1) the wave height distribution due to Stansell et al. (2004) and Zheng et al. (2004) in which the contributions of negative phase derivatives are taken into account fits best with the 20 Hz sampled, 5-point smoothed data; (2) neglecting the contributions of negative phase derivatives results in an expression of the probability of exceeding large wave heights which is closest to the 20 Hz sampled, 5 or 9-point smoothed data; (3) the Rayleigh distribution generally agrees well with our data; the discrepancy between it and early observations mainly comes from the low sampling rate; (4) Forristall's (1984) suggestion of employing Tayfun's (1981) distribution to predict the probability of exceeding given large wave height agrees well with both the 5 and 9-point smoothed data within the range 1.0 ≤ H ≤ 3.0; and (5) the improved joint distribution of wave heights and periods, as well as the marginal distribution of wave periods due to Stansell et al. (2004) and Zheng et al. (2004) are unsatisfactory for broadband waves.