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Median‐Based Unit Weibull (MBUW): A New Variants of Generalized Method of Moments and Percentile Estimators

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  • Iman M. Attia

Abstract

This paper introduces a new two‐parameter unit Weibull distribution defined on the interval (0, 1). It discusses the methodology for deriving its probability density function (PDF), explores various properties, and presents related functions. Numerous figures illustrate the distribution and demonstrate its effectiveness in fitting a wide range of skewed real data. The parameter estimation process using maximum likelihood estimation (MLE) faced challenges, particularly concerning large variance. To address these issues, the generalized method of moments (GMMs) and percentile estimators are introduced as improved alternatives. The paper elaborates on GMMs, percentile estimators, and new variants of both methods for estimating the parameters of the new distribution, supplemented by illustrative analysis of real data.

Suggested Citation

  • Iman M. Attia, 2025. "Median‐Based Unit Weibull (MBUW): A New Variants of Generalized Method of Moments and Percentile Estimators," Journal of Probability and Statistics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljps:v:2025:y:2025:i:1:n:1503091
    DOI: 10.1155/jpas/1503091
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    References listed on IDEAS

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    1. Sajjad Haider Bhatti & Shahzad Hussain & Tanvir Ahmad & Muhammad Aslam & Muhammad Aftab & Muhammad Ali Raza, 2018. "Efficient estimation of Pareto model: Some modified percentile estimators," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-15, May.
    2. Iman M. Attia, 2025. "Median-Based Unit Weibull (MBUW): A New Variants of Generalized Method of Moments and Percentile Estimators," Journal of Probability and Statistics, Hindawi, vol. 2025, pages 1-22, September.
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