Page 106 - Contributed Paper Session (CPS) - Volume 1

CPS1167 Indrani B.
that the life-testing experiment is terminated when the -th failure occurs. With
these notations, we will observe the following progressively censored data:

= ( ,·· ·, , 1 + 1,· · ·, )

1
1
with < ⋯ < 1 < ≤ 1 +1 < ⋯ < . Here, t is the observed values of the
1

variable = … , , 1 +1, … , denoting the m Type-II progressively right
1,

1
censored order statistics from a population with pdf () = (; ) where
(; ) ∈ = ( ) × Ω . Also, = ( , , , ) and Ω is a 4-dimensional
+
1
2
1
2

parametric space. We now consider the maximum likelihood prediction of : ,
j-th order statistic out of a sample of size ; = 1,2, … , ; = 1,2, … , ,

)and =
having observed T . Here, = ( , … , , 1 +1,…, : denote the
1
1
observed value of T and the unobserved value of respectively. Using the
:
fact that the conditional density of : is the same as the density of the j-th
order statistic out of units from the density ()/(1 − ( )), ≥ the

predictive likelihood function (PLF) of and is given by
:
= (, ; )
= | (|,) . (,) (5)
:

= | (| ,) . (,)
:

in which | (|, ) denotes the conditional density of given the
:

observed value of T = t and (,) denotes the density of T . in (5) is then

given by

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