Almost sure limit points of lightly trimmed sums when the distribution function belongs to the domain of partial attraction of a positive semi-stable law

• Autorzy: Vasudeva R. , Srilakshminarayana G.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we obtain the set of all almost sure limit points of lightly trimmed sums, properly normalized, when the underlying distribution function belongs to the domain of partial attraction of a semi-stable law supported on the positive half axis.

Słowa kluczowe

EN

lightly trimmed sums; law of the iterated logarithm; semi-stable law; almost sure limit points

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 1
• Strony: 129--142
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Vasudeva R.

• University of Mysore, Department of Studies in Statistics, Manasagangotri, Mysore-570006, India

autor

Srilakshminarayana G.

• Shri Dharmasthala Manjunatheshwara Institute for Management Development, #1, Chamundi Hill Road, Siddhartha Nagar, Mysore-570011, India

Bibliografia

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• [3] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley Eastern, New Delhi 1972.
• [4] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, 1968.
• [5] H. Kesten and R. Maller, Some effects of trimming on the law of the iterated logarithm, J. Appl. Probab. 41 (2004), pp. 253-271.
• [6] V. M. Kruglov, On the extension of the class of stable distributions, Theory Probab. Appl. 17 (4) (1972), pp. 685-694.
• [7] X. Lu and Y. C. Qi, Chover’s law of the iterated logarithm for trimmed sums, Sankhyā 68 (3) (2006), pp. 488-502.
• [8] T. Mori, Stability for sums of i.i.d. random variables when extreme terms are excluded, Z. Wahrsch. Verw. Gebiete 40 (1977), pp. 159-167.
• [9] R. N. Pillai, Semi-stable laws as limit distributions, Ann. Math. Statist. 42 (2) (1971), pp. 780-783.
• [10] E. Seneta, Regularly Varying Functions, Lecture Notes in Math., Vol. 508, Springer, Berlin 1976.
• [11] R. Shimizu, On the domain of partial attraction of semi-stable distributions, Ann. Inst. Statist. Math. 22 (1970), pp. 245-255.
• [12] R. Vasudeva, Chover’s law of the iterated logarithm and weak convergence, Acta Math. Hungar. 44 (1984), pp. 215-221.
• [13] R. Vasudeva and G. Srilakshminarayana, Chover’s law of the iterated logarithm for trimmed sums when the distribution function belongs to the domain of partial attraction of a semi-stable law, J. Indian Statist. Assoc. 47 (2) (2009), pp. 161-181.
• [14] R. Vasudeva and G. Srilakshminarayana, On strong large deviation results for lightly trimmed sums and some applications, Statist. Probab. Lett. 83 (2013), pp. 1745-1753.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).