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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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Variance01:15

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 The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
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Estimating Population Mean with Known Standard Deviation01:16

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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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Estimating Population Mean with Unknown Standard Deviation01:22

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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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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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Confidence Interval for Estimating Population Mean01:25

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
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Improved exponential type variance estimators for population utilizing supplementary information.

Mujeeb Hussain1, Qamruz Zaman1, Hijaz Ahmad2,3

  • 1Department of Statistics, University of Peshawar, Pakistan.

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|June 3, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces new exponential variance estimators using supplementary information for finite population sampling. These novel estimators demonstrate superior efficiency compared to traditional methods in statistical analysis.

Keywords:
EfficiencyMean square errorOptimumSupplementaryVariance

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Accurate variance estimation in finite populations is crucial for reliable statistical inference.
  • Controlling variation in data can be challenging, necessitating advanced estimation techniques.

Purpose of the Study:

  • To propose an optimal family of exponential variance estimators utilizing supplementary information.
  • To enhance the efficiency of variance estimation in finite population surveys.

Main Methods:

  • Development of a generalized class of exponential variance estimators.
  • Incorporation of known characteristics of supplementary variables.
  • Derivation of bias and mean square error (MSE) expressions.
  • Performance evaluation using real data and simulation studies in R software.

Main Results:

  • The proposed exponential variance estimators show improved efficiency.
  • Specific members of the estimator family were identified and analyzed.
  • Empirical and simulation results confirm the superiority of the new estimators.

Conclusions:

  • The novel family of exponential variance estimators offers significant efficiency gains.
  • The use of supplementary information is effective in improving variance estimation.
  • The proposed methods provide a valuable advancement in finite population sampling techniques.