Yadav, Subhash Kumar; Arya, Diksha; Sharma, Prayas; Zaman, Tolga

The Quest for the improved estimators of population mean is a continuous process to estimate it more efficiently and more closely to the true population mean of the study variable. There are various estimators of population mean in the literature, which estimate it efficiently, but still there is space for more efficient estimators. For improved estimation of population mean of primary variable, we suggest six different searls type ratio estimators utilizing the known auxiliary parameters. We derive the expressions for the biases and the mean squared errors of the introduced estimators for an approximation of degree one. The optimal values of the Searls characterizing constants, which minimize the mean squared errors of the introduced estimators, are obtained. The least value of the mean squared error of the proposed estimators for these optimal values of the characterizing scalars is also acquired. The efficiency of the proposed estimators is compared theoretically with the competing estimators of population mean through their mean squared errors. We derive the efficiency conditions of the proposed estimator for which it is more efficient than the estimators of population mean in competition. These efficiency conditions of the proposed estimators are verified through empirical data and the improvement over the competing estimators is calculated based on the minimum values of the mean squared errors. It is evident from the numerical study that the proposed estimator has the least mean squared error and the highest percentage relative efficiency in comparison to competing estimators. Thus, the proposed estimators are recommended for applications in different areas of applications.

Singh, Poonam; Sharma, Prayas; Singh, Anjali; Zaman, Tolga; Emam, Walid

Reliable statistical inference requires accurate population variance estimate, especially in domains where measurement limitations and intrinsic variability impact data. Applying traditional estimators to skewed or heavy-tailed populations frequently results in inefficient results. We provide a novel class of generalized logarithmic variance estimators that use logarithmic transformations and auxiliary data to stabilize variance and improve estimator performance in order to overcome this constraint. We calculate the suggested estimators' bias and Mean Squared Error (MSE) expressions and assess their effectiveness using comprehensive Monte Carlo simulations with different sample sizes. The suggested estimator, Tr1-, produces a significant reduction in MSE up to 57% increase in efficiency (PRE) at n=600 when compared to the usual estimator. The suggested methodologies resilience and suitability for high-variability situations are further confirmed using real-world datasets. In every context, the findings show that the suggested estimators perform better than the current ones in terms of lower MSE and greater PRE. This research demonstrates how logarithmic transformations may be used to create variance estimators that are more accurate and effective, especially when auxiliary variables are provided.

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.