Page 108 - Contributed Paper Session (CPS) - Volume 1

CPS1167 Indrani B.
∗
− 1

∗
∗
= + log [ ∗ + ] (9)
: 1
in which = (, ) = log(( − 1)/( − ) and and are the PMLEs of
∗
∗

1

and σ respectively. After substituting by : as given in (9), the second
1
equation in (8) becomes
1 (10)
1 − 1 ln− 1
∑( + 1) 1 + ∑ ( + 1) + = + 1
1
1
1
=1 = 1 +1
The third equation in (8) simplifies to
(11)
1 − 2 ln−2
∑ ( + 1) − ∑ ( + 1) = − .
1
1
1
= 1 +1 = 1 +1

is then obtained by using the third equation of (8), (10) and (11) after
∗
substituting by as given in (9) as
:

It can be observed that right hand side of (12) contains which creates some
∗
computational difficulty. Following Thomas and Wilson (1972), we propose the
linearized PMLE ̃ of σ. It is given by

Case 2 : ( = and = 1, … , ) The MMLP : of : is given by (14) in
1
1
which PMLE is obtained by solving
∗
1
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