10 



TABLE 1 



Means and Standard Deviations for Frequency Distributions of Wave Heights 



Sample 



Number of 

 Observations 



Mean 



Standard 

 Deviation 



Average of 

 Means 



Standard 

 Deviation 

 of Means 







ft 



ft 



ft 



ft 



Computed from Weather Bureau Data (Figure la) 



1949 



2811 



7.36 



4.53 







1950 



2724 



7.50 



5.10 



7.69 



0.45 



1951 



2768 



8.45 



5.90 







1952 



2814 



7.40 



4.53 







Computed from Weather Bureau Data (Figure lb) 



1 yr 



2811 



7.36 



4.53 







2 yrs 



5535 



7.51 



4.81 







3 yrs 



8303 



7.82 



5.22 







4 '72 yrs 



12,272 



7.76 



5.07 







Computed from Hydrographic Office Data (Figure 2) 



2 yrs 



528 



3.75 



3.43 







7 yrs 



4830 



3.99 



4.48 







40 yrs 



18,627 



4.71 



. 5.33 







chances out of 100 that the average mean computed, 7.69 ft, will be no further away from the 

 true mean than 1.35 ft.^ (3a = 1.35 ft) for the period 1949 to 1952. 



CONFIDENCE BANDS 



Figure 9 shows confidence bands fitted to the probability density distribution of the 

 Weather Bureau data. These confidence bands, computed according to Kolmogorov's statis- 

 tic, ^° show the interval within which the "true" distribution will fall at a probability level 

 of 99 percent, that is, in 99 cases out of 100 random sampled distributions, the distribution 

 will fall within these bounds. The requirement for the use of Kolmogorov's statistic is that 

 the sampled wave heights be random and that the distribution of wave heights be continuous. 



A plot of the data on probability paper is shown in Figure 9a. The encircled points 

 were computed from the observed wave heights and the solid line represents a logarithmically 

 normal distribution. In this figure the confidence bands were fitted to the observed points. 

 The curve fitted to the probability density distribution shown in Figure 9b was obtained by 

 taking the average probability density of the class intervals at their centers and fairing a 

 curve through these points to make the area under the curve equal to the area under the 



