Page 354 - Contributed Paper Session (CPS) - Volume 2

CPS1885 Karuna G. R. et al.
− + 0 + 0

2
Φ = min { { ( + 1) [ (, ) − (, )]

0≤ ≤
− + +
× [ ( + 2, 0 ) − ( + 2, 0 )]

− + + 2
2 2
− × [ ( + 1, 0 ) − ( + 1, 0 )] × }
ℎ

+ Φ −1 ( − )}. (13)

Substituting the value of , , , and , the optimum strata width
0
ℎ
∗
∗
∗
∗
(OSW)( ) and the OSB ( = ℎ−1 − ) are obtained.
ℎ
ℎ
ℎ

3. Results
We intend to carry out a stratified random sampling on home equity loans
using prior information from the HMEQ data set mentioned in Section 2. To
demonstrate the application of the method, we consider the mortdue study
variable which is found to best-fit Gamma (2P) distribution, with the histogram
and overlay density curve given by Figure 1.
The R package stratifyR [13] was customized by appropriately including
the stratum cost aspect of sample surveys in order to solve the recurrence
relation (12) and (13) to obtain the OSW ( ) and hence the OSB. These results
∗
ℎ
together with the OSS ( ) and the optimum Values of the Objective Function
ℎ
(VOF) for = 2,3, . . ,6 with different stratum measurement costs ( =
ℎ
2,3, . . .,etc. depending on the number of strata) are presented in the Table 1
below.

4. Discussion and Conclusion
This paper presents a method of obtaining the OSB and OSS in stratified
sampling design while taking into account the cost factor with a fixed budget
() and varying measurement cost in each stratum ( ). The procedure is
ℎ
illustrated with a real-world example when the study variable, mortdue, follows
Gamma 2P. The proposed method successfully determines OSB and OSS based
on the stratum costs.

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