共查询到20条相似文献,搜索用时 10 毫秒
1.
Masayuki Uchida 《Annals of the Institute of Statistical Mathematics》1998,50(3):587-601
Let X-m+1, X-m+2,..., X0, X1, X2,..., Xn be a time-homogeneous {0, 1}-valued m-th order Markov chain. The probability distributions of numbers of runs of "1" of length k (k m) and of "1" of length k (k < m) in the sequence of a {0, 1}-valued m-th order Markov chain are studied. There are some ways of counting numbers of runs with length k. This paper studies the distributions based on four ways of counting numbers of runs, i.e., the number of non-overlapping runs of length k, the number of runs with length greater than or equal to k, the number of overlapping runs of length k and the number of runs of length exactly k. 相似文献
2.
Demetrios L. Antzoulakos Stathis Chadjiconstantinidis 《Annals of the Institute of Statistical Mathematics》2001,53(3):599-619
Let {Z
n
, n 1} be a time-homogeneous {0, 1}-valued Markov chain, and let N
n
be a random variable denoting the number of runs of "1" of length k in the first n trials. In this article we conduct a systematic study of N
n
by establishing formulae for the evaluation of its probability generating function, probability mass function and moments. This is done in three different enumeration schemes for counting runs of length k, the "non-overlapping", the "overlapping" and the "at least" scheme. In the special case of i.i.d. trials several new results are established. 相似文献
3.
Serkan Eryilmaz 《Methodology and Computing in Applied Probability》2018,20(2):563-573
A new scheme-distribution-based representation is presented for the cumulative distribution function of the number of success runs of length k in a sequence of exchangeable binary trials. By utilizing this new representation, some stochastic ordering results are obtained to compare success runs. The results are illustrated for beta-binomial distributions of order k. 相似文献
4.
Anant P. Godbole Stavros G. Papastavridis Robert S. Weishaar 《Annals of the Institute of Statistical Mathematics》1997,49(1):141-153
Consider a sequence of n independent Bernoulli trials with the j-th trial having probability pj of success, 1 j n. Let M(n,K) and N(n, K) denote, respectively, the r-dimensional random variables (M(n, k1),..., M(n,kr) and (N(n,k1), ..., N(n, kr)), where K = (k1, k2, ..., kr) and M(n, s) [N(n, s)] represents the number of overlapping [non-overlapping] success runs of length s. We obtain exact formulae and recursions for the probability distributions of M(n, K) and N(n, K). The techniques of proof employed include the inclusion-exclusion principle and generating function methodology. Our results have potential applications to statistical tests for randomness. 相似文献
5.
Waiting Time Distributions Associated with Runs of Fixed Length in Two-State Markov Chains 总被引:3,自引:3,他引:0
M. V. Koutras 《Annals of the Institute of Statistical Mathematics》1997,49(1):123-139
In the present article a general technique is developed for the evaluation of the exact distribution in a wide class of waiting time problems. As an application the waiting time for the r-th appearance of success runs of specified length in a sequence of outcomes evolving from a first order two-state Markov chain is systematically investigated and asymptotic results are established. Several extensions and generalisations are also discussed. 相似文献
6.
James C. Fu W. Y. Wendy Lou Zhi-Dong Bai Gang Li 《Annals of the Institute of Statistical Mathematics》2002,54(4):719-730
The total number of successes in success runs of length greater than or equal to k in a sequence of n two-state trials is a statistic that has been broadly used in statistics and probability. For Bernoulli trials with k equal to one, this statistic has been shown to have binomial and normal distributions as exact and limiting distributions, respectively. For the case of Markov-dependent two-state trials with k greater than one, its exact and limiting distributions have never been considered in the literature. In this article, the finite Markov chain imbedding technique and the invariance principle are used to obtain, in general, the exact and limiting distributions of this statistic under Markov dependence, respectively. Numerical examples are given to illustrate the theoretical results. 相似文献
7.
We consider the distribution of the number of successes in success runs of length at least k in a binary sequence. One important application of this statistic is in the detection of tandem repeats among DNA sequence
segments. In the literature, its distribution has been computed for independent sequences and Markovian sequences of order
one. We extend these results to Markovian sequences of a general order. We also show that the statistic can be represented
as a function of the number of overlapping success runs of lengths k and k + 1 in the sequence, and give immediate consequences of this representation.
AMS 2000 Subject Classification 60E05, 60J05 相似文献
8.
A. N. Frolov 《Journal of Mathematical Sciences》2002,109(6):2229-2240
Let
be a sequence of independent equidistributed random vectors with
. Let
, where
and
denotes the indicator function of the event in brackets. If, for example,
are the gains and
are the indicators of success in repetitions of a game of chance, then
is the maximal gain along head runs (sequences of successes without interruptions) of length j. We investigate the asymptotic behavior of the values
,
, where
is the length of the longest head run in
. We show that the asymptotics of the values
depend significantly on the growth rate of j and that these asymptotics vary from the strong noninvariance (as in the ErdsRéenyi law of large numbers) to the strong invariance (as in the CsöorgRévész strong approximation laws). We also consider the Shepp-type statistics. Bibliography: 17 titles. 相似文献
9.
Serkan Eryilmaz 《Methodology and Computing in Applied Probability》2014,16(1):149-159
This paper is concerned with the distribution of runs associated with claim indicators in a compound binomial risk model. We study the total number of claims, the longest run without claim, the shortest run without claim and the total number of runs up to a fixed period before the occurrence of a ruin. These quantities are potentially useful for an investment strategy of an insurance company and for understanding the behavior of a specific portfolio over time. We obtain recursive equations for the exact distributions of these random variables. We also illustrate the theoretical results with numerical computations. 相似文献
10.
本文考虑了索赔时间间距为Erlang(n)分布带阈限分红策略的更新风险模型的平均折现罚函数,建立了该函数所满足的积分-微分方程及更新方程,最后讨论了更新方程的解. 相似文献
11.
Demetrios L. Antzoulakos 《Annals of the Institute of Statistical Mathematics》1999,51(2):323-330
A general technique is developed to study the waiting time distribution for the r-th occurrence of a success run of length k in a sequence of Markov dependent trials. Sooner and later waiting time problems are also discussed. 相似文献
12.
Chooichiro Asano 《Annals of the Institute of Statistical Mathematics》1965,17(1):331-346
Summary A method is suggested for testing whether two samples observed on a circle are drawn from the same distribution. The proposed
test is a modification of the well-known Wald-Wolfowitz runs test for a distribution on a straight line. The primary advantage
of the proposed test is that it minimizes the number of assumptions on the theoretical distribution.
This study was supported in part by the contract NSF-9968, National Science Foundation; in part by the contract Nonr 2249(05),
(Nr 301–579), the Office of Naval Research, Dept. of the Navy, with The Catholic University of America.
This paper was written while the author was a research associate in the Statistical Laboratory, Department of Mathematics,
The Catholic University of America, during the academic year 1962. 相似文献
13.
14.
Doklady Mathematics - We consider the problem of reconstructing a word from a multiset of its fragments of fixed length. Words consist of symbols from a finite alphabet. The word to be... 相似文献
15.
In this paper we introduce a Markov chain imbeddable vector of multinomial type and a Markov chain imbeddable variable of returnable type and discuss some of their properties. These concepts are extensions of the Markov chain imbeddable random variable of binomial type which was introduced and developed by Koutras and Alexandrou (1995, Ann. Inst. Statist. Math., 47, 743–766). By using the results, we obtain the distributions and the probability generating functions of numbers of occurrences of runs of a specified length based on four different ways of counting in a sequence of multi-state trials. Our results also yield the distribution of the waiting time problems. 相似文献
16.
Doklady Mathematics - In the classical case, the connection between the periodicity of the continued fraction of $$sqrt f $$ and the existence of a fundamental unit of the corresponding... 相似文献
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In the dual risk model, the surplus process of a company is a L′evy process with sample paths that are skip-free downwards. In this paper, the authors assume that the surplus process is the sum of a compound Poisson process and an independent Wiener process. The dual of the jump-diffusion risk model under a threshold dividend strategy is discussed. The authors derive a set of two integro-differential equations satisfied by the expected total discounted dividend until ruin. The cases where profits follow an exponential or mixtures of exponential distributions are solved. Applying the key method of the Laplace transform, the authors show how the integro-differential equations are solved. The authors also discuss the conditions for optimality and show how an optimal dividend threshold can be calculated as well. 相似文献
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