RESUMEN
Environmental monitoring and assessment aim to gather data economically, without bias, using efficient and cost-effective sampling methods. One such traditional method is Ranked Set Sampling (RSS), often employed to achieve observational economy. This article introduces an innovative two-stage sampling approach for ranked set sampling (RSS) to get a more precise estimate of the population mean. Modified Median Quartile Double Ranked Set Sampling (MMQDRSS) highlights the ranked base technique's potential as a cost-effective sampling method. To evaluate the performance of the proposed estimator by using real-life data and conducting a simulation study to compare the relative efficiency of the proposed estimator with some existing methods.
RESUMEN
This research presents a new group of mathematical functions connected to Bernoulli's Lemniscate, using the q-derivative. Expanding on previous studies, the research concentrates on determining coefficient approximations, the Fekete-Szego functional, Zalcman inequality, Krushkal inequality, along with the second and third Hankel determinants for this recently established collection of functions. Additionally, the study derives the Fekete-Szego inequality for the function ξ f ( ξ ) and obtains the inverse function f - 1 ( ξ ) for this specific class. This research advances our understanding in this area and suggests for further exploration.