RESULTS 



An overlay of a normal curve was constructed and used 

 on the probability density curves obtained with the XY 

 recorder. This method was found to have a limited useful- 

 ness since it would not yield results with the desired amount 

 of accuracy in all cases. Cases where it could be used are 

 for curves which do not deviate very much from the overlay. 

 As the deviations become greater it becomes more difficult 

 to estimate the parameters accurately. It was decided not 

 to use an overlay with more than one curve (as described in 

 "Data Reduction Techniques") because, even though the 

 curves were normalized to a standard deviation of 1, the 

 error in setting the input to a value of 1 volt rms can be as 

 much as 10 per cent -- although in most cases it was less 

 than 5 per cent. Such error makes it difficult to estimate 

 the skewness and especially the kurtosis, since the overlay 

 will not fit if the standard deviation is other than 1 . 



With the method of moments it is possible to get 

 estimates of the mean, the standard deviation, the skewness, 

 and the kurtosis. The limited range of amplitudes analyzed 

 (which was thought to be sufficient before the data reduction) 

 causes an error in the calculated moments for those samples 

 which have amplitudes extending beyond three standard de- 

 viations. The error is more evident in the higher (3rd and 

 4th) moments, because of the higher powers of x used in the 

 calculations of these moments. A correction can be applied 

 to the computed skewness and kurtosis. The correction 

 takes into account the "ignored" amplitudes, i.e., it com- 

 pares the computed moment with the moment of a truncated 

 normal distribution. Actually only the moment of kurtosis 

 was corrected, since skewness was not found very fre- 

 quently among the noise samples. 



The hypothesis to be tested is that the noise samples 

 are taken from noise with a gaussian distribution of ampli- 

 tudes. The test used is the same one described on page 21 

 and it is applied to both the skewness and the kurtosis. The 



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