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Skewness01:06

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The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
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Besides mean, the median is a widely used measure of central tendency. Typically, median is defined as the central or middle value of a data set, measured by arranging the data elements in an increasing or decreasing order. Since this middle value is not affected by the precise numerical values of the outliers or fluctuations, it is insensitive to them. Hence, in cases where a data set may have outliers or the extreme values are not known, the median is a better measure of the central tendency...
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Central tendency refers to the central point or typical value of a dataset. It summarizes the data set with a single value that represents the center of its distribution. The three main measures of central tendency are:
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The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Transformation-based median estimation under skewed-symmetric distributions with long-memory data applications.

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New transformation-based median estimators improve accuracy in double-sampling. These methods efficiently use limited data, offering cost-effective and reliable finite population median estimation even with complex data patterns.

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Median estimation in finite populations is crucial for data analysis.
  • Traditional methods can be costly and less accurate with limited auxiliary information.
  • Double-sampling frameworks offer a way to improve efficiency by using supplementary data.

Purpose of the Study:

  • To develop enhanced median estimators for finite populations using a double-sampling framework.
  • To utilize transformation-based methods for efficient use of limited auxiliary information.
  • To assess the accuracy and robustness of the proposed estimators.

Main Methods:

  • Formulation of enhanced median estimators within a double-sampling design.
  • Application of transformation-based methods to leverage auxiliary information.
  • Derivation of first-order approximations for bias and mean squared error.
  • Monte Carlo simulations using real-life datasets and skewed distributions.
  • Investigation of robustness using fractional Gaussian noise (fGn) and ARFIMA models.

Main Results:

  • The proposed estimators demonstrate superior accuracy and efficiency compared to existing methods, as measured by percent relative efficiency (PRE).
  • Performance shows only a minor decrease in efficiency even with increased long-range dependence in auxiliary variables.
  • Graphical analyses confirm the reliability and stability of the estimators.

Conclusions:

  • The new transformation-based median estimators provide stable and economical techniques for median estimation in two-phase sampling.
  • These estimators are effective even when auxiliary information exhibits long-memory or fractal behavior.
  • The methods offer a practical approach to enhance statistical estimation accuracy while managing data collection costs.