HKLlAlilLITV OF TUAKFIC MEASUREMENTS 373 



Letting 



i ' ' n=o 1 — e-'' 



I\^,{.v) (Ix = (''erKdij (4) 



The moiiKMit <j;(Mi(M-atiiii2; fuiu'tioii Mi{a) of y is: 



MM = f r{!/) '/!/ e"' + ('-" 

 Jo 



(5) 



ra — r 



1 -\- a 

 Xeglec'ting terms of oixler hifiluM- than a'-, 



Mj{a) = 1 + a{rK - b') + ^ {Kr + 21/ - 2rK) (0) 



Type II 



Calls of Type II may have either positive or negative errors given by: 



P.<o(.r) dx = '-±^ [/o(-.r) + /i(/ - x) + mi - x) 



+ • • • + /.-i((c - \)i - x)] (7) 



+ </o(-i-) + ^l(^■ - .»•) + g-i{2i - x) + • • • + (/e-i[(c - \)i - x] 



Px>o(.t) (/x = '-^ [/i(f - .1-) + f,{2i - a-) + • • • + /<.(a - .r)] 

 I 



where /„(m' — .r) = probability that a Type II call has length ni — x and 

 ends before the end of the observation period. 



•I n i—x 



= ^ e~ *■ • ■ dx 



i c 



(j.Xni — x) = prol)al)ilit3' that a Type II call starts ni — x before 

 the end of the observation period and ends after 

 the end of the observation period. 



I ni—x 



= ^ e~^^ dx 



