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Robust inference under r-size-biased sampling without replacement from finite population.

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  • 1Department of Civil Engineering, University of Patras, Rion-Patras, Greece.

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Summary
This summary is machine-generated.

Size-biased sampling without replacement shows decreasing bias with increasing sampling fraction, transitioning towards a random sample. A novel likelihood-free method offers robust statistical inference for population parameters and size.

Keywords:
ABC algorithmFinite populationbiased datapetroleum basinweighted distributions

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Area of Science:

  • Statistics
  • Statistical Inference
  • Sampling Theory

Background:

  • Size-biased sampling without replacement presents unique challenges in statistical analysis.
  • Understanding the behavior of such sampling schemes relative to sampling fraction is crucial.

Purpose of the Study:

  • To investigate the characteristics of size-biased samples from finite populations.
  • To develop and evaluate a robust statistical inference method for unknown population parameters and size.

Main Methods:

  • Simulation studies were conducted to analyze sampling behavior.
  • A modified likelihood-free method was employed for statistical inference.

Main Results:

  • Size-biased samples do not represent random samples from the parent or size-weighted distributions.
  • Increasing sampling fraction reduces bias, leading to a transition towards random sampling.
  • The proposed likelihood-free method demonstrated superior robustness compared to existing approaches.

Conclusions:

  • The study clarifies the nature of size-biased sampling and its relationship with sampling fraction.
  • The developed likelihood-free method provides a more accurate approach for statistical inference in these scenarios.