On distributions of record ranges in nonstandard situations

Authors

  • Igor V. Belkov

Abstract

The record theory is an important part of the probability theory and mathematical statistics and has many applications in various fields of knowledge. Most of the known methods deal with the standard model (when the initial random variables are independent and identically distributed). However, various nonstandard models also show some practical interest. In this article, a number of results for distributions and properties of record ranges and sample ranges are obtained for initial sequences of random variables in some nonstandard situations, namely when the variables of the initial sequence have the Laplace distribution or the mixture of two geometric distributions on the positive and negative semi-axes. The converse problem is also investigated, namely: the aforementioned distributions can be characterized by independency of W (1) and W (2) - W (1), where W (1), W (2),... are sample ranges in the sequences of initial random variables, if the constant X0 = 0 is added before the initial sequence. Refs 9.

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References

1. Невзоров В.Б. Рекорды. Математическая теория. М.: Фазис, 2000. 244c.

2. Arnold B.C., Balakrishnan N., Nagaraja H.N., Records (John Wiley & Sons, New York, 1998, 314 p.).

3. Nevzorov V.B., Ahsanullah M., Record Statistics. International Encyclopedia of Statistical Sciences (Springer-Verlag, Berlin, Heidelberg, 2011, 1195-1202).

4. Chandler K.N., The distribution and frequency of record values, J. R. Stat. Soc., Ser. B 14, 220-228 (1952).

5. Tippett L.H.C., On the extreme individuals and the range of samples taken from a normal population, Biometrika 17, 364-387 (1925).

6. Houchens R.L., Record Value Theory and Inference (Ph.D. Dissertation, University of California, Riverside, California, 1984).

7. Tukey J.W., Comparing individual means in the analysis of variance, Biometrics 5(2), 99-114 (1949).

8. Arnold B.C., Balakrishnan N., Nagaraja H.N., A First Course in Order Statistics. In Ser. Society of Industrial and Applied Mathematics (Philadelphia, 2008, xxiv+280 p.).

9. Бельков И.В., Невзоров В.Б. О рекордных величинах в последовательностях выборочныхразмахов // Вестн. С.-Петерб. ун-та. Математика. Механика. Астрономия. 2017. Т.4(62) [в печати].

Published

2020-08-20

How to Cite

Belkov, I. V. . (2020). On distributions of record ranges in nonstandard situations. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 4(3), 387–393. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/8611

Issue

Section

Mathematics