of bandwidth about 55 c/s, with N given by the equation N = 



6.7/, where / is the bandwidth. The equation is obtained 



o o 



from Appendix B, using a time constant T = 2.3 seconds. 



The overlay method was not used extensively because 

 of the complexity that comes from considering different 

 values of N and also different combinations of skewness and 

 kurtosis in the same sample. A method using computed 

 moments of the curves is described next; it was felt that 

 this method would yield accurate values of the mean, 

 standard deviation, skewness, and kurtosis. 



METHOD OF MOMENTS 



The method of moments is basically a general method 

 of forming estimates of the parameters of a distribution by 

 means of a set of measured sample values. The first few 

 moments of the actual distribution are calculated and these 

 are used as estimates of the moments of the parent population. 

 On the basis of these moments a suitable theoretical dis- 

 tribution curve is selected. For any particular distribution 

 curve the moments are functions of the parameters of that 

 curve. The parameters are determined and tests of sig- 

 nificance are made on the skewness and kurtosis. 



The moments about the origin are defined as 5 



m ' = £ p.(x)x. (6) 



r v i> 



i 

 where p^(x) is the probability that a value selected at ran- 

 dom from the population will lie in the i-th class. The 

 variate x with which we are concerned may be discrete or 

 continuous. 



The moment 



m 1 ' - E P t ^ x t (7) 



18 



