15 



APPENDIX 1 

 PEARSON-TYPE DISTRIBUTION CURVES 



A set of curves that may be fitted to different frequency distributions was compiled by 

 the statistician Karl Pearson. The theoretical derivation and calculations necessary for 

 fitting these curves are described in Reference 11. The curve type which best fits a frequency 

 distribution may be identified from criteria calculated on the basis of the values of the 

 moments [i-. 



The steps for identifying and computing the constants for^the fitting of the curve shown 

 in Figure 6 are given here. The numerical values are those for the frequency distribution of 

 the Weather Bureau data for the iy^-yr period, Figure 1. 



The moments measured about the mean value of the distribution are: 



Ml =^ = [3] 



= 13.68 [4] 



N 



1 fz^ 



N 



40.27 [5] 



2 f z^ 

 ,.4=^^ = 593.6 [6] 



where z represents the deviation of the actual value / from the mean, 



/ is the frequency, and 



A' is the total frequency of the sample. 

 The criteria ^^, 13^, and K computed from the preceding moments are: 



/3, =i-3- = 0.6336 [7] 



/S,=-^ = 3.173 [8] 

 2 



' 1 ■ 2 ' ^ -0.3596 [9] 



4(4/32 -3,g^)(2^2- 3,3 J " ^) 



Since the criterion K is negative, it identifies Pearson's Main Type I Curve as the most 

 suitable one. This curve is defined by the equation 



