APPENDIX B: 



DETERMINATION OF NUMBER OF DATA POINTS OF 

 EACH SAMPLE 



The application of the x 8 test to our type of data was 

 desired as a means of testing the "goodness of fit" of the 

 data to certain theoretical distributions and, in particular, 

 the fit to the gaussian distribution. There is some difficulty 

 in applying this test directly because N 3 the total number of 

 points in our sample, is not known. However it is possible 

 to obtain an estimate of N which can be used. The estimate 

 of N is also used in determining whether the moments of 

 the distribution, that are calculated by the method of moments, 

 are significant at a given probability level. The estimate 

 of N is found as follows. 



From reference 1 use 



a _ (3/877)^ 



n f Tw(x)Ax V 



where / is the input bandwidth of the signal, T is the 

 sampling interval or a time constant which gives an equivalent 

 averaging, and w(x) is the value of probability density ob- 

 tained from the PDA. The ct 2 is the normalized variance of 

 the estimate of the probability density, and is not to be 

 confused with the variance of the distribution of amplitudes 

 of the input signal. In reference 1, N is given as 



(B-2) 



a Ax 



n 



Here N represents the total number of times that the input 

 signal enters the amplitude interval Ax at the (x) of interest. 

 After combining equations B-l and B-2 we have 



N = ^n Tw{j [ ) - 2.9fjw(x) (B-3) 



(3/8irF 



43 



