Wave statistics and their relations with spectral width parameters were investigated for about 140 surface wave records of deepwater waves with an ultrasonic wave recorder at the ports of Sakata, Habu, Hamada and Naha around the Japan Coast.
　Furthermore, we developed the estimating method of the wave period parameters and spectral width parameter νfrom spectral width parameter ε and the zero-crossing period, based on the Rice's theory.
　According to the results in this paper, the followings are concluded.
　1) The significant wave height is the most statistically stable in the wave height parameters, while the average wave period T1 (m0/m1) in the wave period parameters.
　2) The significant wave period T1/3 is the best parameter to be correlated with the peak wave period Tp corresponding to the spectal peak.
　3) The estimated peak wave period Tp1 from the Rice's theory is more statistically stable than Tp. The relation between T1/3 and Tp1 is given by Tp1=1.10 T1/3 with the error of about 5 to 6%.
　4) T1, the estimate of T1 from the Rice's theory, is statiscally stable and is the relation T1/T1=1.03 is approximately correct.
　5) According to the run analysis of wave records, from η rms sequences in a wave record we can find the nonstationality only for 2-4 hours before the fully-developed state, but we can't find that from skewness √β1 and kurtosis β2 sequences.