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APPENDIX 



The two partial deviations of In L (Equation (11)) are 



a InL 



N 



-N I 

 da i=2 N 



-U-i- k«- aLi 



1 - e 



-oA. 



Ni 



% Z -z + tx - (% - h) 



I— I - 



= (Al) 



d InL 

 dp 



-N I 



N 



i=c+i N 



In u x + 



\-j~\ ln l i 



1 - 



/ u W 



k-i 



- In 



'20 1 



Wi 



i— r 



= (A2) 



where A^ = t { - t i _ 1 and u x ~ 3. 



Both Equations (Al) and (A2) depend on the proportion NJN rather than the absolute counts (iV/s). In 



order to have a unique solution of a and (1, it is necessary to have 



a 2 In L „ - , 3 2 InL ^ 



— n o < and — nn9 < 0. 



da 2 dft 2 



Moreover, the conditions 



(A3) 



and 



hm — > 0, hm — < 



o — o da o— oo da 



.. d InL .. d InL 



hm — — — > 0, hm — — -— < 

 is— o dp p~oo dp 



(A4) 



guarantee a positive solution of a and p. Equation (A3) leads to the following constraints 

 406 



