On the Joint Distribution of Precedences and Exceedances for the Two-Sample Problem

Authors

  • Eugenia Stoimenova Bulgarian Academy of Sciences, Bulgaria
  • Narayanaswamy Balakrishnan McMaster University, Canada

DOI:

https://doi.org/10.17713/ajs.v40i1&2.207

Abstract

This paper studies the joint behaviour of precedences of one sample with respect to a threshold from the other sample and exceedances of second sample with respect to a threshold from the first sample. Exact joint distribution of the number of precedences and exceedances is derived for the case of equal distributions of the two samples.

References

Arnold, B. C., Balakrishnan, N., and Nagaraja, H. N. (2008). A First Course in Order Statistics. Reprint of the 1992 original edition. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).

Bairamov, I., and Eryilmaz, S. (2008). Joint behaviour of precedences and exceedances in random threshold models. Australian and New Zealand Journal of Statistics, 50, 209-216.

Balakrishnan, N., and Ng, H. K. T. (2006). Precedence-Type T-tests and Applications. Hoboken, NJ: John Wiley & Sons.

David, H. A., and Nagaraja, H. N. (2003). Order Statistics (3rd ed.). Hoboken, NJ: John Wiley & Sons.

Stoimenova, E., and Balakrishnan, N. (2010). A class of exceedance-type statistics for the two-sample problem. ((submitted for publication))

van der Laan, P., and Chakraborti, S. (2001). Precedence tests and Lehmann alternatives. Statistical Papers, 42, 301-312.

Wesołowski, J., and Ahsanullah, M. (1998). Distributional properties of exceedance statistics. Annals of the Institute of Mathematical Statistics, 50, 543-565.

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Published

2016-02-24

How to Cite

Stoimenova, E., & Balakrishnan, N. (2016). On the Joint Distribution of Precedences and Exceedances for the Two-Sample Problem. Austrian Journal of Statistics, 40(1&2), 157–166. https://doi.org/10.17713/ajs.v40i1&2.207

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Articles