Zaman, Tolga; Sozen, Caglar

The neutrosophic framework provides a convenient way to represent uncertainty and indeterminacy through interval-valued quantities. This paper proposes quantile-based neutrosophic combined and separate regression estimators for the finite population mean under stratified random sampling. Building on the combined and separate quantile regression estimators of Koç and Koç (Axioms 12:713, 2023), we incorporate neutrosophic (interval) versions of stratum-specific quantile regression components and derive approximate bias and mean squared error (MSE) expressions using first-order linearization. We provide efficiency conditions under which the proposed neutrosophic estimators improve upon their classical counterparts and we evaluate performance via (i) a simulation study comparing classical and neutrosophic estimators, and (ii) a real-data illustration based on monthly high–low index data (2010–2024) for the S&P 500, Nikkei 225, and DAX, where MSE bounds are reported for the proposed neutrosophic estimators. Across the considered experiments, the neutrosophic separate estimator at the 0.50 quantile attains the smallest MSE among the reported competitors, suggesting that a median-oriented robust component combined with stratification can be effective when observations are imprecise. Limitations and directions for further extensions are discussed.

Zaman, Tolga; Sozen, Caglar

Classical statistical methods cannot directly incorporate measurement uncertainties and indeterministic elements into the model, leading to estimation errors and biases, especially in environmental datasets. Neutrosophic statistics, on the other hand, offers a broader approach that does not only rely on exact values, but also includes ambiguous, incomplete and conflicting information. In this study, we propose a new neutrosophic ratio-type estimator for estimating the population mean using monthly temperature data for Turkey for the period 2010-2022. This study proposes neutrosophic multivariate exponential estimators considering two auxiliary attributes. The mean square error equations of all proposed neutrosophic exponential estimators are obtained theoretically. Some conditions of neutrosophic multivariate exponential estimators are considered and the properties of these estimators are studied. The effectiveness of the proposed neutrosophic exponential estimators is analyzed using neutrosophic temperature data. In addition to real data analysis, extensive simulation studies are conducted under various scenarios to evaluate the performance of the estimators. The results demonstrate that the proposed estimators perform effectively under uncertainty and can be successfully applied in forecasting environmental variables.

Zaman, Tolga; Iftikhar, Soofia; Sozen, Caglar; Sharma, Prayas

Earthquake is a fierce and unavoidable natural disaster. The study of aftershocks following an earthquake provides a comprehensive understanding of seismic activity, making it an important area of research. Although it is important to mention that the use of the Poisson distributed population, to estimate the mass mean of rare events such as earthquakes, has been little studied in the literature. In this context, this study proposes a new class of logarithmic type ratio estimators for estimating the mean of a Poisson distributed population in a simple random sampling without replacement. The proposed estimators are obtained using the logarithmic transformation of the ratio estimator, and the expressions for the mean square error (MSE) are also derived to the first order of approximation. The study demonstrates that the proposed logarithmic type estimators are more efficient than the existing estimators, both theoretically and empirically. The Empirical evidence from a real data study conducted using earthquake data from Turkey confirms the superiority of the proposed estimators over the existing estimators. The study provides valuable insights for researchers and practitioners working with Poisson distributed populations and requiring ratio estimators using simple random sampling without replacement.