共查询到20条相似文献,搜索用时 31 毫秒
1.
V. B. Nevzorov 《Vestnik St. Petersburg University: Mathematics》2013,46(4):170-174
Record values are very popular in probability and mathematical statistics. There are many books and papers concerned with classical record values and record times, i.e., records in sequences of independent equally distributed random variables. In recent times, new types of record values (records in the F α-scheme, record values in sequences of unequally distributed random variables, records with confirmations, exceedance record values) have been proposed and examined. The present paper proposes another record scheme (so-called “records with constraint”). Various cases are studied in which these records may be useful. For these record values, we give their joint density functions and discover some of their properties. For particular cases of utmost importance, when the initial random variables are independent and have equal exponential distribution, we obtain fairly simple representations of records with constraints as sums of independent equally distributed random terms. 相似文献
2.
Ismihan G. Bairamov 《Annals of the Institute of Statistical Mathematics》2000,52(3):448-458
New characterizations for the exponential distribution are given in terms of record values and the probabilities of finite sums of independent and identically distributed nonnegative random variables provided that the underlying distribution is either new better than used or new worse than used. 相似文献
3.
In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed. 相似文献
4.
Tomasz J. Kozubowski 《Annals of the Institute of Statistical Mathematics》2000,52(2):231-238
We show that every strictly geometric stable (GS) random variable can be represented as a product of an exponentially distributed random variable and an independent random variable with an explicit density and distribution function. An immediate application of the representation is a straightforward simulation method of GS random variables. Our result generalizes previous representations for the special cases of Mittag-Leffler and symmetric Linnik distributions. 相似文献
5.
V. B. Nevzorov 《Journal of Mathematical Sciences》1988,43(6):2830-2833
A result is found for discrete random variables, which lets one express the distribution of k-th record values in terms of the distribution of sums of independent summands.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 133–137, 1987. 相似文献
6.
Jason Fulman 《Annals of Combinatorics》2006,10(3):319-332
Bolthausen used a variation of Stein’s method to give an inductive proof of the Berry-Esseen theorem for sums of independent,
identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of
a random representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions.
Received March 11, 2005 相似文献
7.
A. N. Chuprunov 《Journal of Mathematical Sciences》1995,76(1):2110-2117
The paper deals with sums of independent and identically distributed random variables defined on some probability space which
are multiplied by random coefficients. These coefficients are the values of independent random variables defined on another
probability space. We obtain conditions for the weak convergence of weighted sums, for almost all coefficients, to some infinitely
divisible distribution. The limit distribution for these sums is found.
Supported by the Russian Foundation for Fundamental Research (grant No. 93-011-16099).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, 1993. 相似文献
8.
Malay Ghosh Gutti Jogesh Babu Nitis Mukhopadhyay 《Probability Theory and Related Fields》1975,33(1):49-54
For a sequence of independent and identically distributed positive random variables, the almost sure convergence of sums of maxima (when suitably normalized) to appropriate constants is proved for both bounded and unbounded random variables. A similar result is also proved for sums of minima of such variables. 相似文献
9.
A. S. Fainleib 《Journal of Theoretical Probability》1998,11(3):609-619
The purpose of this paper is to investigate small values of semi-additive functions and its application to find an upper bound of concentration functions for the sums of independent identically distributed random variables. 相似文献
10.
A. N. Chuprunov 《Lithuanian Mathematical Journal》1995,35(1):42-52
The paper deals with maxima and sums of independent random variables. These random variables are the values of independent
identically distributed stochastic processes at a random point in time. We obtain conditions for their weak convergence, at
almost all points in time to the same infinitely divisible distribution and describe the limit distribution for these sums.
Some applications of these results to statistics are considered.
This work was supported by the Russian Foundation for Fundamental Research (grant No. 93-011-16099).
Research Institute of Mathematics and Mechanics, Kazan State University, 17 Universitetskaya St., Kazan, 420008, Russia. Translated
from Lietuvos Matematikos Rinkinys, Vol. 5, No. 1, pp. 52–64, January–March, 1995.
Translated by A. N. Chuprunov 相似文献
11.
12.
A. I. Martikainen 《Journal of Mathematical Sciences》1992,61(1):1879-1885
A sequence of independent random variables with zero mean generates, by applying to it the A. V. Skorokhod representation, a sequence of random arguments of a Wiener process. At the proof of limit theorems for sums of independent random variables with the use of this representation, there arises the question of the stability of the sequence of the random arguments. In the paper the law of the iterated logarithms yields exact bounds for the oscillation of this sequence.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 83–91, 1989. 相似文献
13.
Fotis Loukissas 《Journal of Theoretical Probability》2012,25(4):913-924
In this paper, we investigate the precise large deviations for sums of independent identically distributed random variables with heavy-tailed distributions. We prove asymptotic relations for non-random sums and for random sums of random variables with long-tailed distributions. We apply the results on two useful counting processes, namely, renewal and compound-renewal processes. 相似文献
14.
LiXin Zhang 《中国科学 数学(英文版)》2016,59(4):751-768
Classical Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers. In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng (2008), we introduce the concept of negative dependence of random variables and establish Kolmogorov’s and Rosenthal’s inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations. As an application, we show that Kolmogorov’s strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite. 相似文献
15.
O. V. Rusakov 《Vestnik St. Petersburg University: Mathematics》2017,50(2):153-160
The definition of pseudo-Poissonian processes is given in the famous monograph of William Feller (1971, Vol. II, Chapter X). The contemporary development of the theory of information flows generates new interest in the detailed analysis of behavior and characteristics of pseudo-Poissonian processes. Formally, a pseudo-Poissonian process is a Poissonian subordination of the mathematical time of an independent random sequence (the time randomization of a random sequence). We consider a sequence consisting of independent identically distributed random variables with second moments. In this case, pseudo-Poissonian processes do not have independent increments, but it is possible to calculate the autocovariance function, and it turns out that it exponentially decreases. Appropriately normed sums of independent copies of such pseudo-Poissonian processes tend to the Ornstein–Uhlenbeck process. A generalization of driving Poissonian processes to the case where the intensity is random is considered and it is shown that, under this generalization, the autocovariance function of the corresponding pseudo-Poissonian process is the Laplace transform of the distribution of that random intensity. Stochastic choice principles for the distribution of the random intensity are shortly discussed and they are illustrated by two detailed examples. 相似文献
16.
在本文中我们讨论了不同分布负相关随机变量加权和的强定律.在一个有限矩生成函数的条件下,一些有关负相关随机变量加权和的强定律被获得.这些结果推广了Soo HakSung[4]关于独立同分布随机变量的相应结论.我们的结果也概括了Mi Hwa Ko和Tae SungKim[7]获得的相关结论,同时使得Nili Sani H R和Bozorgnia A[9]所取得的结果更加形象. 相似文献
17.
G. P. Chistyakov 《Journal of Mathematical Sciences》1999,93(3):480-483
A new asymptotic representation for the distribution function of the normalized sums of not necessary identically distributed
random variables in the Lyapunov CLT is established. Asymptotically proper constants in the Berry-Esseen inequality are obtained.
Bibliography: 13 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 228, 1996, pp. 349–355. 相似文献
18.
19.
We here propose some new algorithms to compute bounds for (1) cumulative density functions of sums of i.i.d. nonnegative random variables, (2) renewal functions and (3) cumulative density functions of geometric sums of i.i.d. nonnegative random variables. The idea is very basic and consists in bounding any general nonnegative random variable X by two discrete random variables with range in hN, which both converge to X as h goes to 0. Numerical experiments are lead on and the results given by the different algorithms are compared to theoretical results in case of i.i.d. exponentially distributed random variables and to other numerical methods in other cases. 相似文献
20.
We consider independent geometric distributed random variables which satisfy suitable hypotheses. We study large and moderate deviations for their empirical means, and we illustrate applications of the large deviation results for the weak record values of i.i.d. discrete random variables. 相似文献