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Statistical inference and data analysis for inverted Kumaraswamy distribution based on maximum ranked set sampling

Amal S Hassan1, Samah A Atia2

  • 1Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt.

Scientific Reports
|October 25, 2024
PubMed
Summary
This summary is machine-generated.

Maximum ranked set sampling with unequal samples (MRSSU) improves parameter estimation for the inverted Kumaraswamy distribution. This advanced ranked set sampling method offers superior performance over traditional ranked set sampling (RSS) in simulations and real-world data analysis.

Keywords:
Bayes estimationInverted Kumaraswamy distributionMarkov Chain Monte CarloMaximum likelihood estimationMaximum ranked set sampling with unequal size

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Area of Science:

  • Statistics
  • Probability Theory
  • Statistical Modeling

Background:

  • Ranked set sampling (RSS) is an efficient data collection technique.
  • Maximum ranked set sampling with unequal samples (MRSSU) is a modification of RSS.
  • Parameter estimation for distributions is crucial in statistical analysis.

Purpose of the Study:

  • To estimate parameters of the inverted Kumaraswamy distribution using MRSSU and RSS designs.
  • To compare the performance of MRSSU and RSS estimation techniques.
  • To investigate both maximum likelihood and Bayesian estimation methods.

Main Methods:

  • Utilized Maximum Likelihood Estimation (MLE) and Bayesian estimation.
  • Employed non-informative (Jeffreys) and informative (gamma) priors for Bayesian analysis.
  • Applied squared error and minimum expected loss functions.
  • Conducted simulation studies using root mean squared error and relative bias.
  • Employed the Metropolis-Hastings algorithm for Bayes point estimates.

Main Results:

  • MRSSU estimators demonstrated significantly better performance than RSS estimators.
  • This improvement was consistent across both simulation studies and real geological data analysis.
  • The study evaluated parameter estimation accuracy under different sampling designs.

Conclusions:

  • MRSSU is a more efficient sampling design for parameter estimation compared to RSS, especially for larger sample sizes.
  • The findings are applicable to statistical modeling and data analysis in various fields.
  • The inverted Kumaraswamy distribution parameter estimation is robust under the MRSSU design.