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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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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
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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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Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
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Improved estimation of population distribution function using twofold auxiliary information under simple random

Sohaib Ahmad1, Sardar Hussain2, Aned Al Mutairi3

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

Heliyon
|February 1, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces improved statistical estimators for population distribution functions using auxiliary information. The new methods demonstrate superior accuracy and efficiency compared to existing techniques.

Keywords:
BiasDistribution functionMSEPRETwofold auxiliary information

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Area of Science:

  • Statistics
  • Statistical Inference
  • Survey Sampling

Background:

  • Accurate estimation of population distribution functions (DF) is crucial in statistical analysis.
  • Existing methods may lack efficiency when incorporating auxiliary information.
  • Simple random sampling is a fundamental technique, but enhancements are needed.

Purpose of the Study:

  • To propose enhanced families of estimators for population DF estimation.
  • To utilize twofold auxiliary information within simple random sampling.
  • To improve the precision and efficiency of distribution function estimation.

Main Methods:

  • Development of novel estimator families incorporating auxiliary variables.
  • Empirical validation using four real-world datasets.
  • Simulation studies to assess estimator performance and precision.

Main Results:

  • The proposed estimators achieved minimum mean square error (MSE).
  • Enhanced percentage relative efficiency (PRE) was observed compared to existing estimators.
  • A specific recommended family consistently outperformed others across datasets.

Conclusions:

  • The suggested estimator families offer significant improvements in estimating population distribution functions.
  • The enhanced methods provide superior performance in terms of MSE and efficiency.
  • The findings highlight the practical utility of the proposed estimators in statistical surveys.