SAMPLE 

 NO. 



X 2 



s 



9i 



g 2 



13 



X 



X(5%) 



X(5%) 



14 



31.2 







15 



17.5 







16 



32.6 







17 



X 





X(5%) 



18 



18.2 







30 



14.7 







32 



2.8 







34 



14.4 







37 



3.9 







41 



2.7 







42 



32.4 





X(5%) 



49 



40 







66 



3.3 







68 



38 







83 



5.4 







104 



2.2 







112 



42 







132 



5.5 







134 



X 







135 



X 



X(l%) 





147 







X(5%) 



150 



X 





X(5%) 



TABLE 5. CURVES FOR WHICH x : 

 WAS COMPUTED, COMPARED 

 WITH RESULTS BY METHOD OF 

 MOMENTS. THE X's INDICATE 

 THOSE CURVES WHICH REJECTED 

 THE HYPOTHESIS. 



the 3rd and 4th moments were significant at the 5 per cent 

 or 1 per cent level. Generally the results of the chi-square 

 test agree with the results of the method of moments. 



Only one hypothesis was tested and this was that the 

 noise samples were taken from a gaussian distribution 

 with the mean equal to zero and the standard deviation 

 equal to one. A better hypothesis is to assume that the 

 distribution is gaussian with a mean x - m and standard 

 deviation s - s , where m and s are estimated from the 

 sample itself. 



Table 6 shows parameters for several noise samples 

 which were selected by the overlay normal curve as very 

 closely approximating a gaussian curve. The four computed 

 moments of each sample are given (the mean, the standard 

 deviation, the skewness, and the kurtosis). The ratio of 

 the skewness and kurtosis to the square root of their 

 variances are given. The computed value of \ 2 is given 

 for comparison. All three methods agree that these samples 



35 



