Page 350 - Contributed Paper Session (CPS) - Volume 2

CPS1885 Karuna G. R. et al.

Sample allocation scheme for gamma
populations based on survey cost
1
Karuna G. Reddy , M.G.M. Khan
2
1 Centre for Survey Research and Methods, Australian National University, Australia
2 School of Computing, Information and Mathematical Sciences, The University of South
Pacific, Fiji

Abstract
Under stratified sampling design, surveyors usually aim to estimate certain
charateristics, such as mean for a study variable, for a survey population. With
the intention of producing precise estimates, efforts are usually based on a
fixed total sample size () where the stratum costs are kept to a constant of
$1/. However, with most sample surveys nowadays governed by a total
cost or budget, this paper presents a method of determining the stratum
sample sizes based on fixed sampling cost () with varying per unit stratum
costs ( ). Incorporating the cost factor, the idea of constructing optimum
ℎ
strata boundaries are subsequently used to determine stratum sample sizes
under Neyman allocation. To illustrate the applicability of the method, we
utilize the home equity loan data set and consider a study variable called
mortdue (mortgage due) that follows Gamma distribution.

Keywords
Stratified random sampling; survey cost; optimum strata boundaries; optimum
sample sizes; mathematical programming problem; dynamic programming
technique; gamma distribution.

1. Introduction
The determination of optimum strata boundaries (OSB) is inherently
linked to determining the stratum sample allocations. Considering that the
stratification variable is a continuous study variable (), a parametric-based
approach can be utilized to determine optimal sample sizes (OSS) by cutting
the distribution of the data into OSB points. When data is not available, it’s
distribution and parameters can be hypothesized apriori based on previous or
past surveys. The basic idea involved is to determine the OSB in such a manner
that the strata becomes as internally homogenous as possible. Obtaining the
OSB points with minimum total stratum variances [4] enables surveyors
achieve maximum precision with reasonably low stratum sample sizes, thereby
reducing the cost of sampling.
To determine the OSB, some notable techniques that have been widely
used are the Cumulative Root Frequency method ( √) of [5, 6], the

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