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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. Giovanni Maria Giorgi & Michele Crescenzi, 2005. "A look at the Bonferroni inequality measure in a reliability framework," Econometrics 0507004, University Library of Munich, Germany.
    3. Giovanni Maria Giorgi & Riccardo Mondani, 2005. "Sampling distribution of the Bonferroni inequality index from exponential population," Econometrics 0507008, University Library of Munich, Germany.
    4. 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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    3. 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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    6. 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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