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Related Concept Videos

Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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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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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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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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Estimating Population Standard Deviation01:26

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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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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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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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A new improved generalized class of estimators for population distribution function using auxiliary variable under

Sohaib Ahmad1, Kalim Ullah2, Erum Zahid3

  • 1Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan.

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|April 3, 2023
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Summary
This summary is machine-generated.

Researchers developed improved estimators for finite population distribution functions and means using auxiliary variables under simple random sampling. These new estimators demonstrate superior performance and higher efficiency compared to existing methods.

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Accurate estimation of finite population characteristics is crucial in statistical surveys.
  • Existing estimators may not fully leverage auxiliary information for improved precision.

Purpose of the Study:

  • To propose a generalized class of improved estimators for finite population distribution functions and means.
  • To enhance estimation accuracy by utilizing auxiliary variables under simple random sampling.

Main Methods:

  • Derivation of bias and mean squared error (MSE) expressions for the proposed estimators.
  • Development of two specific improved estimators from the generalized class.
  • Empirical evaluation using three real data sets and a simulation study.

Main Results:

  • The proposed generalized class includes two improved estimators, with the second offering greater gains.
  • The novel estimators achieved minimum MSE and higher percentage relative efficiency.
  • Performance comparison showed the proposed estimators outperformed existing counterparts.

Conclusions:

  • The developed generalized class of estimators is effective for improving finite population distribution function and mean estimation.
  • The proposed estimators offer a statistically significant advancement over traditional methods.
  • Empirical evidence supports the practical utility and superior performance of the new estimators.