A Note on Generalized Inverses of Distribution Function and Quantile Transformation

DOI: 10.4236/am.2012.312A289   PDF   HTML   XML   5,852 Downloads   8,097 Views   Citations

Abstract

In this paper we study the relations of four possible generalized inverses of a general distribution functions and their right-continuity properties. We correct a right-continuity result of the generalized inverse used in statistical literature. We also prove the validity of a new generalized inverse which is always right-continuous.

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C. Feng, H. Wang, X. Tu and J. Kowalski, "A Note on Generalized Inverses of Distribution Function and Quantile Transformation," Applied Mathematics, Vol. 3 No. 12A, 2012, pp. 2098-2100. doi: 10.4236/am.2012.312A289.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] R. B. Ash, “Probability and Measure Theory,” 2nd Edition, Academic Press, San Diego, 2000.
[2] A. W. Van der Vaart, “Asymptotic Statistics,” Cambridge University Press, New York, 1998.
[3] E. Langford, “Quartiles in Elementary Statistics,” Journal of Statistics Education, Vol. 14, No. 3, 2006. www.amstat.org/publications/jse/v14n3/langford.html
[4] P. K. Andersen, O Borgan, R. D. Gill and N. Keiding, “Statistical Models Based on Counting Processes,” Springer, New York, 1993. doi:10.1007/978-1-4612-4348-9
[5] S. I. Resnick, “Extreme Values, Regular Variation, and Point Processes,” Springer, New York, 1987.
[6] P. Embrechts, C. Klüppelberg and T. Mikosch, “Modeling Extremal Events for Insurance and Finance,” Springer, New York, 1997.
[7] A. J. McNeil, R. Frey and P. Embrechts, “Quantitative Risk Management: Concepts, Techniques, Tools,” Princeton University Press, Princeton, 2005.
[8] A. W. Marshall and I. Olkin, “Life Distributions,” Springer, New York, 2007.
[9] R. Durrett, “Probability: Theory and Examples,” 4th Edition, Cambridge University Press, New York, 2010. doi:10.1017/CBO9780511779398

  
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