1 < 



g^-t,) |20r _ ± 



| — I 



.2 JV 1- e-^i-^-i) 



(A5) 



and 



1 < 



I — I 



/ u \-p 



In 



'20^ 



M T 



W 



e°( u i- f i) 



i=c+i N 



ti-i t 



In 



ti 



t- 



i-l 





Mi 



« 



i-l, 



(A6) 



After algebraic manipulation, it was easy to see that Equation (A4) was true for this truncated exponential 

 and the Pareto MLE. We used an iterative procedure to select the MLE of a and /J, which satisfies not 

 only Equation (A3) but also the constraints of Equations (A5) and (A6). 

 The partial derivations in each entry of matrix A (Equation (12)) are 



'201" 



3 2 lnP, 

 da 2 



e«(«i-*i) 



- 5 — - e**i + ( Ml _ tf- 



u. 



e .<.,-.,. g ' . i 



3 2 In ^ 



dp 2 



In 



'20 1 



Wi 



201" 



Ui 



e"(»i- ( i) 



g-d^-y j^j' 3 _ i 



and 



d 2 \nP, V J v \uJ \u x 



dadp 



e-dH-t,) I? -]" _ i 



407 



