共查询到20条相似文献,搜索用时 15 毫秒
1.
Peng Zhao Ping Shing Chan Hon Keung Tony Ng 《Journal of statistical planning and inference》2011,141(5):1737-1743
In this paper, we provide sufficient conditions on weighted coefficients under which the peakedness comparison between weighted sums of independent random variables can be carried out. These results extend and enrich the existing peakedness results in the literature including those presented by Proschan (1965) and Ma (1998). 相似文献
2.
AbstractLet {Xn, n ? 1} be a sequence of negatively superadditive dependent (NSD, in short) random variables and {bni, 1 ? i ? n, n ? 1} be an array of real numbers. In this article, we study the strong law of large numbers for the weighted sums ∑ni = 1bniXi without identical distribution. We present some sufficient conditions to prove the strong law of large numbers. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for NSD random variables is obtained. In addition, the complete convergence for the weighted sums of NSD random variables is established. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables. 相似文献
3.
On the strong convergence for weighted sums of random variables 总被引:1,自引:1,他引:0
Soo Hak Sung 《Statistical Papers》2011,52(2):447-454
A strong convergence result is obtained for weighted sums of identically distributed negatively associated random variables
which have a suitable moment condition. This result improves the result of Cai (Metrika 68:323–331, 2008). 相似文献
4.
Soo Hak Sung 《Statistical Papers》2012,53(1):73-82
In this paper, we obtain a complete convergence result for weighted sums of negatively dependent random variables under mild conditions of weights. This result generalizes and improves the result of Zarei and Jabbari (Stat Papers doi:, 2009). Our result also extends the result of Taylor et al. (Stoch Anal Appl 20:643–656, 2002) on unweighted average to a weighted average. 相似文献
5.
《统计学通讯:理论与方法》2012,41(2):281-306
AbstractIn this paper, we obtain the exponential-type inequalities for maximal partial sums of negatively superadditive dependent (NSD) random variables, which extends the corresponding results for independent and negatively associated (NA) random variables. Using these inequalities, we further investigate the weak convergence of the M-estimators in the generalized linear model with NSD errors, which generalize and improve the corresponding results of the independent random errors to that of NSD random errors. 相似文献
6.
ABSTRACTIn this article, a complete convergence result and a complete moment convergence result are obtained for the weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results are also obtained under the extended negatively orthant dependent setup. In particular, the complete convergence result generalizes and improves the related known works in the literature. 相似文献
7.
Yongfeng Wu 《统计学通讯:理论与方法》2013,42(20):5977-5989
ABSTRACTThe authors discuss the convergence for weighted sums of pairwise negatively quadrant dependent (NQD) random variables and obtain some new results which extend and improve the result of Bai and Cheng (2000). In addition, we relax some restrictions of the conditions in their result. Some new methods are used in this article which differ from that of Bai and Cheng (2000). 相似文献
8.
In this note, we introduce a new class of dependent random variables (henceforth rvs), together with some its basic properties. This class includes independent rvs and pairwise negatively dependent rvs. Some extensions of Ranjbar et al. (2008) are discussed. The complete convergence for the new class of rvs is also proved, and some results of Beak and Park (2010) are extended to this class conveniently. 相似文献
9.
In this article, the complete convergence for weighted sums of extended negatively dependent (END, in short) random variables without identical distribution is investigated. In addition, the complete moment convergence for weighted sums of END random variables is also obtained. As an application, the Baum–Katz type result for END random variables is established. The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables. 相似文献
10.
U. Kamps 《Statistical Papers》1990,31(1):233-237
The exponential distribution is characterized by means of the distribution of a weighted sum of independent, identically distributed random variables. The conditions considered turn out to be sufficient in the case of two random variables only. 相似文献
11.
《Journal of statistical planning and inference》1986,14(1):15-28
A two-parameter class of discrete distributions, Gould series distributions, generated by expanding a suitable parametric function into a series of Gould polynomials is discussed. A Gould series distribution occurs in fluctuations of sums of interchangeable random variables and particularly as the distribution of (i) the duration of the game in the theory of games of chance, (ii) the busy period in queueing processes and (iii) the time of emptiness in dam and storage processes. The probability generating function and the factorial moments of the Gould series distributions are obtained in close forms. It is pointed out that the name of the generalized general binomial (binomial or negative binomial) distribution of Consul and Jain is justified by the form of its generating function. Finally it is shown that the generalized general binomial distribution, under certain mild conditions, is the only member of the Gould series distributions which is closed under certain mild conditions, is the only member of the Gould series distributions which is closed under convolution 相似文献
12.
ABSTRACTFor widely dependent random variables, we present some results on the strong convergence of weighted sums, including results on almost surely (a.s.) and complete convergence. To this end, we verified some Borel–Cantelli lemmas of the widely dependent random variables. The above-mentioned random variables contain common negatively dependent random variables, some positively dependent random variables, and some others; therefore, the obtained results extend and improve some existing results. 相似文献
13.
Changjun Yu 《统计学通讯:理论与方法》2017,46(2):591-601
This paper investigates tail behavior of the randomly weighted sum ∑nk = 1θkXk and reaches an asymptotic formula, where Xk, 1 ? k ? n, are real-valued linearly wide quadrant-dependent (LWQD) random variables with a common heavy-tailed distribution, and θk, 1 ? k ? n, independent of Xk, 1 ? k ? n, are n non-negative random variables without any dependence assumptions. The LWQD structure includes the linearly negative quadrant-dependent structure, the negatively associated structure, and hence the independence structure. On the other hand, it also includes some positively dependent random variables and some other random variables. The obtained result coincides with the existing ones. 相似文献
14.
Let {Xn, n ? 1} be a sequence of asymptotically almost negatively associated (AANA, for short) random variables which is stochastically dominated by a random variable X, and {dni, 1 ? i ? n, n ? 1} be a sequence of real function, which is defined on a compact set E. Under some suitable conditions, we investigate some convergence properties for weighted sums of AANA random variables, especially the Lp convergence and the complete convergence. As an application, the Marcinkiewicz–Zygmund-type strong law of large numbers for AANA random variables is obtained. 相似文献
15.
Lorenzo Hernández Jorge Tejero Alberto Suárez Santiago Carrillo-Menéndez 《Statistics and Computing》2014,24(3):377-397
A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations are obtained both when the number of terms in the sum is deterministic and when it is random. The zeroth order approximation is the percentile of the maximum term in the sum. Higher orders in the perturbative series involve the right-truncated moments of the individual random variables that appear in the sum. These censored moments are always finite. As a result, and in contrast to previous approximations proposed in the literature, the perturbative series has the same form regardless of whether these random variables have a finite mean or not. For high percentiles, and specially for heavier tails, the quality of the estimate improves as more terms are included in the series, up to a certain order. Beyond that order the convergence of the series deteriorates. Nevertheless, the approximations obtained by truncating the perturbative series at intermediate orders are remarkably accurate for a variety of distributions in a wide range of parameters. 相似文献
16.
Complete moment convergence for weighted sums of sequence of extended negatively dependent (END) random variables is discussed. Some new sufficient and necessary conditions of complete moment convergence for weighted sums of END random variables are obtained, which improve and extend some well-known results in the literature. 相似文献
17.
18.
Consider a sequence of NA identically distributed random variables with the underlying distribution in the domain of attraction of the normal distribution. This paper proves that law of the iterated logarithm holds for sequences of NA random variables. 相似文献
19.
AbstractIn this paper, we consider the complete convergence for weighted sums of negatively superadditive-dependent (NSD) random variables without assumptions of identical distribution. Some sufficient and necessary conditions to prove the complete convergence for weighted sums of NSD random variables are presented, which extend and improve the corresponding ones of Naderi et al. As an application of the main results, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of NSD random variables is also achieved. 相似文献