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Bonferroni Curve and the related statistical inference

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  • Pundir, Sudesh
  • Arora, Sangeeta
  • Jain, Kanchan

Abstract

Two measures of inequality, viz. the Bonferroni Curve and the Bonferroni index are studied. It is shown that these have some relationship with Lorenz Curve, Gini ratio and certain concepts used in reliability, life testing and renewal theory. The problem of testing of Bonferroni Curve and its ordinate(s) is discussed in the multivariate set-up. The variance-covariance structure of the vector of Bonferroni Curve ordinates is derived and a simulation exercise is done.

Suggested Citation

  • Pundir, Sudesh & Arora, Sangeeta & Jain, Kanchan, 2005. "Bonferroni Curve and the related statistical inference," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 140-150, November.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:2:p:140-150
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    References listed on IDEAS

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    1. Mahesh Chandra & Nozer D. Singpurwalla, 1981. "Relationships Between Some Notions Which are Common to Reliability Theory and Economics," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 113-121, February.
    2. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
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    2. Porro Francesco, 2014. "How We Can Evaluate the Inequality in Flint," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 119-128, December.
    3. Ziqing Dong & Yves Tillé & Giovanni M. Giorgi & Alessio Guandalini, 2021. "Linearization and variance estimation of the Bonferroni inequality index," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1008-1029, July.
    4. Abdus Saboor & Muhammad Nauman Khan & Gauss M. Cordeiro & Marcelino A. R. Pascoa & Juliano Bortolini & Shahid Mubeen, 2019. "Modified beta modified-Weibull distribution," Computational Statistics, Springer, vol. 34(1), pages 173-199, March.
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    7. Hassan S. Bakouch & Abdus Saboor & Muhammad Nauman Khan, 2021. "Modified Beta Linear Exponential Distribution with Hydrologic Applications," Annals of Data Science, Springer, vol. 8(1), pages 131-157, March.

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