A Π-BASED EXPONENTIAL TYPE ESTIMATOR FOR SIMPLE RANDOM SAMPLING
ARCENG IV. INTERNATIONAL MEDITERRANEAN SCIENTIFIC STUDIES CONGRESS, Antalya, Turkey, 22 - 23 August 2026, pp.1-9, (Full Text)
- Publication Type: Conference Paper / Full Text
- City: Antalya
- Country: Turkey
- Page Numbers: pp.1-9
- Dokuz Eylül University Affiliated: Yes
Abstract
This study considers an
exponential-type estimator for estimating the population mean under simple
random sampling, where the base of the exponential function is not fixed at the
conventional constant e but is instead treated as a deterministic calibration
parameter. This perspective allows the exponential transformation to be
interpreted within a broader class of estimators whose responsiveness can be
adjusted through the choice of the base. As an illustrative case, the constant
π is adopted, which results in a deterministic rescaling through ln(π) while
preserving the monotonicity of the transformation. Approximate expressions for
the bias and mean squared error (MSE) of the proposed estimator are derived and
compared with those of the classical exponential estimator. Analytical
conditions under which the proposed form achieves efficiency gains are also
obtained. The theoretical results are supported by Monte Carlo simulation
experiments and an application to real COVID-19 data. The findings suggest that
the proposed π-based specification can yield lower MSE than the conventional
estimator under certain coefficient-of-variation configurations. The proposed
π-based specification highlights the potential of treating the exponential base
as a flexible calibration parameter in survey estimation.