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Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities...
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Statistical inference for a novel distribution using ranked set sampling with applications.

Hassan M Aljohani1

  • 1Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.

Heliyon
|December 17, 2024
PubMed
Summary
This summary is machine-generated.

This study introduces a ranked set sampling technique for the Unit Generalized Rayleigh distribution, simplifying complex symmetrical and asymmetrical data analysis. This method enhances parameter estimation for financial and actuarial risk modeling.

Keywords:
Least squaresMaximum product spacingMean squared errorsRanked set samplingRayleigh distribution

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Area of Science:

  • Statistics
  • Actuarial Science
  • Financial Mathematics

Background:

  • Analyzing symmetrical and asymmetrical data requires specific probability density functions, posing challenges in statistical modeling.
  • The Unit Generalized Rayleigh distribution offers flexibility for modeling both symmetric and asymmetric data, with applications in finance, insurance, and reliability.

Purpose of the Study:

  • To apply the ranked set sampling (RSS) technique for estimating parameters of the Unit Generalized Rayleigh (UGR) distribution.
  • To evaluate the performance of different estimation procedures and risk measures using RSS in actuarial and financial contexts.

Main Methods:

  • Utilizing the ranked set sampling design for parameter estimation of the UGR model.
  • Computing various estimation procedures and risk measures.
  • Conducting Monte Carlo simulation experiments to validate the RSS design and assess estimator performance through bias and mean squared errors.

Main Results:

  • The ranked set sampling design proved effective for parameter estimation in the Unit Generalized Rayleigh distribution.
  • Simulation experiments demonstrated the performance of the proposed estimators, with computed average bias and mean squared errors.
  • Real-world financial applications validated the potential and superiority of the RSS estimators.

Conclusions:

  • Ranked set sampling is a valuable technique for enhancing the analysis of complex data using the Unit Generalized Rayleigh distribution.
  • The proposed method offers improved parameter estimation and risk assessment in actuarial and financial studies.
  • The study highlights the practical utility and effectiveness of RSS in real-world financial applications.