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Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution

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  • Josmar Mazucheli
  • André Felipe Berdusco Menezes
  • Sanku Dey

Abstract

Inference based on popular maximum-likelihood estimators (MLEs) method often provide bias estimates of order O(n-1)$ \mathcal {O}(n^{-1})$. Such bias may significantly affect the accuracy of estimates. This observation motivates us to adopt some bias-corrected technique to reduce the bias of the MLE from order O(n-1)$ \mathcal {O}(n^{-1})$ to order O(n-2)$ \mathcal {O}(n^{-2})$. In this paper, we consider the unit-gamma distribution which has some properties similar to the Beta distribution. This distribution is obtained by transforming a Gamma random variable but it has not been widely explored in the literature. We adopt a “corrective” approach to derive second-order bias corrections of the MLEs of its parameters. Additionally, we also consider the parametric Bootstrap bias correction. Monte Carlo simulations are conducted to investigate the performance of proposed estimators. Our results revels the bias corrections improve the accuracy of estimates. Finally, two real data examples are discussed to illustrate the applicability of the unit-Gamma distribution.

Suggested Citation

  • Josmar Mazucheli & André Felipe Berdusco Menezes & Sanku Dey, 2018. "Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(15), pages 3767-3778, August.
  • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:15:p:3767-3778
    DOI: 10.1080/03610926.2017.1361993
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    Cited by:

    1. Guillermo Martínez-Flórez & Hector W. Gomez & Roger Tovar-Falón, 2021. "Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model," Mathematics, MDPI, vol. 9(16), pages 1-20, August.
    2. Guillermo Martínez-Flórez & Roger Tovar-Falón & Carlos Barrera-Causil, 2022. "Inflated Unit-Birnbaum-Saunders Distribution," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    3. Suelena S. Rocha & Patrícia L. Espinheira & Francisco Cribari‐Neto, 2021. "Residual and local influence analyses for unit gamma regressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 137-160, May.
    4. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.

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