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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 32 | Number 2 | Year 2016 | Article Id. IJMTT-V32P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V32P516

Strong limiting regions of hypertension vector sequences of order statistics


N. Vadiraja, H. Vishnu Hebbar
Abstract

This paper finds a limiting region for the patient’s hypertension behavior based on several values above the cut off value of blood pressure taking together , by properly normalizing the vector sequences comprising of moving maxima (Yk(n) ) , moving second maxima (Sk(n) ) ,…, moving Kth maxima Kk(n) , K being the Kth order statistics , using Borel Cantelli lemma, which is meaningful in taking the decision on hypertension for treatment and so on. However, for ease of computation, results are proved for Yk(n) and Sk(n) , under certain conditions on F and k(n). The results are just stated for K order statistics.

Keywords
Almost sure limit set; Moving maxima; Moving second maxima; Vector sequence.
References

[1] De Haan,L. and A. Hordijk (1972). On the rate of growth of sample maxima, Ann. Math. Statist. 43, 1185- 1196.
[2] Gut, A. (1990). Limit of sample maxima, Statist. Probab. Lett. 9, 331-336.
[3] Hebbar,H.V. and N. Vadiraja (1996-97). Almost sure limit points of sequences of moving maxima under power normalization,JISPS, 3,17-34.
[4] Hebbar,H.V. and N. Vadiraja (1997). Limit points of sequences of moving maxima, Statist.Probab. Lett. 34,13-18.
[5] Oertega, J. and M. Wschebor. (1984). On the sequence of some random sequences, Stochastic Process. Appl. 16, 85-98.
[6] Rothmann, M.D. and R.P. Russo (1991). Strong limiting bounds for a sequence of moving maxima. Statist. Probab. Lett. 11, 403-410.

Citation :

N. Vadiraja, H. Vishnu Hebbar, "Strong limiting regions of hypertension vector sequences of order statistics," International Journal of Mathematics Trends and Technology (IJMTT), vol. 32, no. 2, pp. 99-111, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V32P516

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