Íslenskar landbúnaðarrannsóknir - 01.03.1977, Page 77

MAXIMUM LIKELIHOOD ESTIMATION 75
The first derivatives of the logarithms of
the likelihood function yields the equations:
dL _ ni+n 4 _ n3 2ns s _ n6 (1-s2)______________
dp p 1-p-q q + 2ps 1-p-q + qs + ps2
— = n2 _ n3 n5 _ n6 (1-s)
dq q 1-p-q q + 2ps 1-p-q + qs + ps2,
dL _ _ 2n4+ n5 + 2n5 p n6 (q+2ps)
ds 1-s q + 2ps 1-p-q + qs + ps2
and the negative expectations of the second
derivatives are as föllows:
_ ,d2L.
-E (-r-z-
dp
Nl{i + -pJ—} + n2Í-<LíL2 + 4+ 5' +
p 1-p-q p q + 2ps
(l-s2)2
1-p-q+qs+ps2
-E(
dpdq'
n i {-—-— } + n2{2s(1:s1. +
(l-s2)(1-s)
1-p-q
q + 2ps 1-p-q+qs+ps'
-E(
d2L
dpds
.Nl[Í3SlzlL + >
q + 2ps 1-p-q+qs+ps
q(1-s)2+ 2s
d2L
"E llT-2")
dq
N i {— + } + N 2 {—r-
q 1-p-q q + 2ps
(1-s)
1-p-q+qs+ps2
-E (
d2L
dqds
, __ M r 2p (1-s) (1-S)Z y
2 q + 2ps 1-p-q+qs+ps2
,e(4
E(dsz)
r'q + 2ps 4p2 (1-s) + (q + 2ps) 2
2 1-s q + 2ps 1-p-q+qs+ps2