. La revue technique de Bell System . Ains presque constant, à environ 0.82, jusqu'à ce que b devienne environ 0.40ZO 3 0.35 tr ^ 0.30 a 0.250.200.15 -^ ^ /! N ^ li ^ c^ 1 1 k^ X 1 . , 1 j ^ /i b = t.a o.e-j< 0.6-^ IJL 111 OUA- / h ///, 4 W 0 0.1 0.2 0.3 0,4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 RÉCIPROQUE DU MODULE, P Fig. 4.1—fonction de distribution pour la réciproque du module (r = 0 à 1.4). 0.7, après quoi l'emplacement de la valeur maximale se déplace assez rapidlyto environ 0.71 pour ft = 1. Pour les cas 6=0 et b = 1, il est facile de trouver, en distinguant (4.7)et (4.8), que le

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. The Bell System technical journal . ains nearly constant, at about 0.82, until b becomes about 0.40ZO 3 0.35 tr ^ 0.30 a 0.250.200.15 -^ ^ ^ /! N ^ li ^ c^ 1 1 k^ X 1 . , 1 j ^ /I b = t.a o.e-j< 0.6-^ Ijl 111 oaU- / h ////, 4 w 0 0.1 0.2 0.3 0, 4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 RECIPROCAL OF THE MODULUS, P Fig. 4.1—Distribution function for the reciprocal of the modulus (r = 0 to 1.4). 0.7, after which the location of the maximum value moves rather rapidlyto about 0.71 for ft = 1. For the cases 6=0 and b = 1, it is easily found, by differentiating (4.7)and (4.8), that the maximum ordinates are located at r = /2/3 = 0.8165and at r = l//2 = 0.7071 respectively; and hence, by (4.7) and (4.8).that the values of these maximum ordinates are (3/3/2 exp (—3/2) = PROBABILITY FUNCTIONS FOR COMPLEX VARIATE 339 0.8198 and (4/V27r) exp (-1) = 0.5871 respectively. These results forthe cases 6 = 0 and 6=1 agree with the corresponding curves in Fig. 4.1.. 0.20 0.23 0.32 0.36 0.40 RECIPROCAL CF THE MODULUS, T Fig. 4.2—Distribution function for the reciprocal of the modulus {r = 0.2 to 0.5). For the general case where b has any fixed value in the 6-range (0^6^ 1), it is apparently not possible to obtain an explicit expression (in closed form)either for the value of r at which P{r;b) has its maximum value or for the 340 BELL SYSTEM TECH NIC A L JOURNAL maximum value of P(r;b). However, as shown in Appendix C, curves ofthese quantities versus b can be computed, in an indirect manner, bytemporarily taking b as the dependent variable and taking T, defined by(4.6), as an intermediate independent variable. For let Tc denote thecritical value of r, that is, the value of r at which P(r;b) has its maximumvalue; and let Tc denote the corresponding value of T, whence, by (4.6), Tc= b/{-b-)r (4.9) Then, computed by means of the formulas derived in Appendix C, Fig. 4.3gives a curve of Vc and a curve of Max P{r;b), each versus b. From thesecurves i

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