REILLY ET AL.: POPULATION ASSESSMENT OF GRAY WHALE 



APPENDIX 2.— VARIANCE ESTIMATION 



Forn, = (X£M/g  24: 



!0.464 ;re=l 

 0.000 ; n = 2,3 from Reilly et al. (1980). 

 0.612 ;n > 4 



var (n,) = (24A ; ) 2  {L\arE\n\\, by the Delta Method (Seber 1973). 



Forrc, = (Ln)  p;. 



var (n) = ip) 2 var (En,) + {1m) 2 var (p,), 

 where var(En,) = 2 var(n ; ) as above, assuming cov {n p n^) — 0, and 



var(p,) = (Sp/8a) 2 var(P) + (8p/8p) 2 var(a) + 2(<5p/5/3) (Sp/Sp) 

 X cov (a,/?), by the Delta Method, and 



var (a), var (/?), and cov(a,/3) are estimated as in Greenwood and 

 Durand(1960). 

 ForiV, = {Xny/Inj  0.)  «(*): 



var (JVJ is approximated by the Delta Method (as in var (h) and 



var (p ; )), with component variances 



var (0)^0(1 - 6)/n, 



var { n(/e» = (-C p /C;) 2 var (C p ) + (l/C p ) 2 var (CJ, 



l ;arCC p ) = C / ,(l-C p )/«, 



var (C s ) = var (nj, in which 



var (n b ) = & (n fl /E/i n ) 2  Evar (p nfc ), and 



var (p at j - E(pJ (1 + pj/n a . 



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