Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Different estimation methods for the unit inverse exponentiated weibull distribution

  • Amal S Hassan (Faculty of Graduate Studies for Statistical Research, Cairo University) ;
  • Reem S Alharbi (Faculty of Science, Department of Statistics, King Abdulaziz University)
  • Received : 2022.09.29
  • Accepted : 2023.01.03
  • Published : 2023.03.31
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Abstract

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

Keywords

Acknowledgement

We gratefully acknowledge the editor and referees for their meaningful suggestions and comments relating to the improvement of the paper.

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