16 



where y is the ordinate at the mode,* 



X is the distance from the mode, and 



are computed from the equations which follow and 





[11] 



First a parameter r must be evaluated 



= 5.934 [12] 



(6 + 3/3^ - 28^) 



^1 + ^2 =W^2 i^i(^+2)2+ 16(r+ 1)1=22.71 [13] 



.^,;n2=i<|(^-2)!r(r+2)j/L_ -A— ^^ \ [14] 



/3i(r+ 2)^ + 16(r+ 1) 



When (i^ is positive, ot, is the root corresponding to the plus sign; if ^^ is negative, m^ is the 

 root corresponding to the minus sign. 

 For our numerical example 



n\ = 0.441 



m^ =3.493 

 Finally m, m„ 



° a, + fl„ m + m r (m + 1) r {m + 1) 



^ ^ (m^ + m,) 1 '^ ^ ^ 



Tables of the gamma function are given in the reference 11. With the use of logarithms, y. 

 was computed to be 1404, and the mode of the distribution was found to be at 3.99 ft. 

 Equation [10] becomes: 



2/ = 1357(l+^) .(1--:^ [16] 



\ 2.55/ \ 20.2/ 



This gives the frequency distribution in terms of a class interval of unit length. Therefore 

 for a class interval of 1.6 ft, the frequency would be 2171. Since the probability density 

 distribution was desired, y was divided by A'. 



♦The mode is the most frequent or common value; it will correspond to the maximum ordinate of the frequency 

 distribution. 



