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Related Concept Videos

Distributions to Estimate Population Parameter01:26

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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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The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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A new auxiliary variables-based estimator for population distribution function under stratified random sampling and

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Population distribution function estimation is crucial in sample surveys.
  • Existing methods using auxiliary data with stratified random sampling and non-response techniques have limitations.

Purpose of the Study:

  • To improve the accuracy of population distribution function estimation.
  • To maximize accuracy under combined stratified random sampling and non-response conditions.

Main Methods:

  • Utilized a study variable and two auxiliary variables (mean and ranks).
  • Introduced new classes of estimators for stratified random sampling with non-response.
  • Conducted theoretical and numerical estimations on real-world populations.

Main Results:

  • Proposed estimators demonstrated superior performance compared to existing methods.
  • Simulation analysis confirmed significant improvements in estimation accuracy.
  • Comparative graphs validated the effectiveness of the new estimators.

Conclusions:

  • The developed estimators offer enhanced accuracy for population distribution function estimation.
  • The study provides a robust framework for handling non-response and sampling in surveys.
  • Findings support the practical application of these improved estimation techniques.