Page 352 - Contributed Paper Session (CPS) - Volume 2

CPS1885 Karuna G. R. et al.
where, represents the overhead cost, i.e., costs for administration and
0
conducting training for interviewers. The term gives the cost of collecting
0
information per unit in ℎ stratum.
ℎ
Then the problem of determining the optimum allocation of sample size
; ℎ = 1, 2, . . . , for which (̅ ) in (2) is minimum for a fixed total cost is
ℎ

given by

1 1
2 2
Minimize ∑ ( − )
ℎ ℎ

ℎ=1 ℎ ℎ

subject to + ∑ , = (4)
ℎ ℎ
0
ℎ=1

Ignoring finite population correction, (4) reduces into a more simplified
objective function, which is the same as minimizing

∑ √ (5)
ℎ ℎ
ℎ
ℎ=1

Let (); ≤ ≤ be the frequency function of the mortdue variable on
which OSB are to be constructed and OSS to be determined. Since the study
variable is known and integrable, , and can be obtained as a function
2
ℎ
ℎ
ℎ
of the boundary points and ℎ−1 by using the following expressions:
ℎ
ℎ
= ∫ (); (6)
ℎ
ℎ−1

1 ℎ
2
2
2
= ∫ () − (7)
ℎ
ℎ

ℎ ℎ−1

1 ℎ
where = ∫ () (8)
ℎ

ℎ ℎ−1

ℎ
and ( ℎ−1 , ) are the boundaries of ℎ stratum.
ℎ
Using maximum likelihood (MLE) approach, Gamma (2P) happens to be
the best-fit statistical distribution of the mortdue study variable. Notably,
researchers have found that real-life quantities such as income/wealth,
insurance claims, credit risk of loans losses and sugarcane production happen
to generally have statistical properties of the Gamma distribution [2, 3, 12, 14].
Thus, mortdue is estimated with the following Gamma 2P density function with
parameters:

1
, > 0; = 2.923291, = 25228.35, (9)
(; ; ) = −1 −

Γ()

where is a shape parameter and θ is the scale parameter and Γ() is a
Gamma function defined by

341 | I S I W S C 2 0 1 9