Weighted Laws of Large Numbers for A Class of Independent Summands

• Autorzy: Pakes Anthony G.

Identyfikatory

DOI

10.37190/0208-4147.41.1.5

• Języki publikacji: EN

Abstrakty

EN

This paper obtains a necessary and sufficient condition for a weak law of large numbers for weighted averages of positive-valued independent random variables whose distributions belong to a class which includes the F^α-scheme of record theory. Additional general conditions are found under which the weak law extends to a strong law with the same norming. Examples show these conditions can be fulfilled, and that if they are not, then the weighted averages exhibit multiple growth rates.

Słowa kluczowe

EN

weak laws of large numbers; strong laws of large numbers; weighted sums; relative stability; regular variation

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2021
• Tom: Vol. 41, Fasc. 1
• Strony: 55--75
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Pakes Anthony G.

• Department of Mathematics & Statistics, University of Western Australia, 35 Stirling Highway, Crawley WA, Australia 6009

Bibliografia

• [1] A. Adler and A. G. Pakes, On relative stability and weighted laws of large numbers, Extremes 20 (2017), 1-31.
• [2] A. Adler and A. G. Pakes, Weak and one-sided strong laws for random variables with infinite mean, Statist. Probab. Lett. 142 (2018), 8-16.
• [3] A. Adler and R. Wittmann, Stability of sums of independent random variables, Stoch. Processes Appl. 52 (1994), 179-182.
• [4] N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Cambridge Univ. Press, Cambridge 1987.
• [5] Y. S. Chow and H. Teicher, Probability Theory: Independence, Interchangeability, Martingales, Springer, New York 1978.
• [6] B. V. Gnedenko and A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, MA, 1954.
• [7] T. Nakata, Weak laws of large numbers for weighted independent random variables with infinite mean, Statist. Probab. Lett. 109 (2016), 124-129.
• [8] T. Nakata, Exact laws of large numbers for independent Pareto random variables, Bull. Inst. Math. 12 (2017), 325-338.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).