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Related Concept Videos

Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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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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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
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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.
William S. Gosset (1876–1937) of the...
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Sampling Distribution01:12

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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What are Estimates?01:06

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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Memory type general class of estimators for population variance under simple random sampling.

Anoop Kumar1, Anshika2, Walid Emam3

  • 1Department of Statistics, Central University of Haryana, Mahendergarh, Haryana, 123031, India.

Heliyon
|September 9, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces novel memory-type estimators for population variation in simple random sampling (SRS). These estimators, using exponentially weighted moving averages (EWMA), outperform traditional methods in simulations and real-world data analysis.

Keywords:
62D05Efficiency performanceExponentially weighted moving averages (EWMA)Mean square error (MSE)Memory-based methodsPopulation varianceSimple random sampling

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Area of Science:

  • Statistics
  • Survey Methodology
  • Statistical Inference

Background:

  • Estimating population variation is crucial in statistical surveys.
  • Traditional estimators may not fully leverage temporal data.
  • Memory-type approaches offer potential for improved efficiency in surveys.

Purpose of the Study:

  • To propose a new class of memory-type estimators for population variation in simple random sampling (SRS).
  • To evaluate the bias and mean square error (MSE) of the proposed estimators.
  • To compare the efficiency of the new estimators against existing methods.

Main Methods:

  • Development of memory-type estimators utilizing exponentially weighted moving averages (EWMA).
  • Derivation of analytical expressions for bias and mean square error (MSE).
  • Validation through simulation studies on hypothetical populations and real-life data.

Main Results:

  • The proposed memory-type estimators demonstrate superior efficiency compared to conventional and other memory-type estimators.
  • Theoretical efficiency conditions were established for the novel estimators.
  • Simulation and real-data applications confirmed the practical superiority of the proposed approach.

Conclusions:

  • The novel memory-type estimators offer a more efficient approach to estimating population variation in SRS.
  • EWMA-based estimators effectively utilize current and past survey information.
  • The proposed methods provide a valuable advancement for temporal survey analysis.