On Sums of Lognormal Random Variables

Approximations to the characteristic function of the lognormal distribution are computed and used to calculate approximations to the density of sums of lognormal random variables.     

On Sums of Bernoulli Random Variables Modulo 3

Mathematical Notes -     

关于弱收敛非负随机变量序列的逆矩

在2 δ阶矩有限时,对一类非负弱收敛随机变量列,给出了成立的充分条件,推广了[2]中的结果并严密了其中主要结果定理3,定理4的证明．     

On Some Approximations for Sums of Independent Random Variables

Lithuanian Mathematical Journal - In this paper, we generalize a result on approximation of sums by sums with a fixed number of summands in [V. Bentkus, A new method for approximation in...     

On Stochastic Orders for Sums of Independent Random Variables

In this paper, it is shown that a convolution of uniform distributions (a) is more dispersed and (b) has a smaller hazard rate when the scale parameters of the uniform distributions are more dispersed in the sense of majorization. It is also shown that a convolution of gamma distributions with a common shape parameter greater than 1 is larger in (a) likelihood ratio order and (b) dispersive order when the scale parameters are more dispersed in the sense of majorization.     

On the LIL for Self-Normalized Sums of IID Random Variables

Let be i.i.d. random variables and let, for each and . It is shown that a.s. whenever the sequence of self-normalized sums S _n /V _n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if      

On Sums of Overlapping Products of Independent Bernoulli Random Variables

We find the exact distribution of an arbitrary remainder of an infinite sum of overlapping products of a sequence of independent Bernoulli random variables.     

On Sums of Products of Bernoulli Variables and Random Permutations

Let {X _k } _k1 be independent Bernoulli random variables with parameters p _k . We study the distribution of the number or runs of length 2: that is . Let S=lim _n S _n . For the particular case p _k =1/(k+B), B being given, we show that the distribution of S is a Beta mixture of Poisson distributions. When B=0 this is a Poisson(1) distribution. For the particular case p _k =p for all k we obtain the generating function of S _n and the limiting distribution of S _n for .     

Moderate Deviations for Random Sums of Heavy-Tailed Random Variables

Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E（X1） and let {N（t）; t ≥0} be a random process taking non-negative integer values with finite mean λ（t） = E（N（t）） and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P（（X1 ＋… ＋XN（t）） -λ（t）μ 〉 x） uniformly for x ∈[γb（t）, ∞） are obtained, where γ〉 0 and b（t） can be taken to be a positive function with limt→∞ b（t）/λ（t） = 0.     

On the Moment Convergence for Weighted Sums of Pairwise NQD Random Variables

Under the condition of h-integrability with respect to an array of weights, the moment convergence for weighted sums of pairwise negative quadrant dependent random variables is studied. The authors obtain a new result, and solve the open problem in Sung et al. ,(2008) and improve the corresponding theorem of Cabrera and Volodin (2005).     

相依随机变量列的随机和的中心极限问题

本文给出阵列框架下的相依随机变量列的随机和弱收敛和稳定收敛的充分必要条件，我们的结果与经典结果相似并囊括此方向上的所有已知结果．     

特殊重尾随机变量随机和的大偏差

文献[1]对于一些经典重尾随机变量的随机和大偏差作了有意义的讨论,本文则讨论了另外一些同样有用的重尾随机和的大偏差.     

NA随机变量加权和的收敛性

利用Rosenthal型最大值不等式,得到了NA随机变量加权和的Marcinkiewicz-Zygmund强大数定律和完全收敛性,所获结果推广和改进了一些文献中相应的结果.     

On Moments of the Maximum of Normed Partial Sums of p--mixing Random Variables

In this paper, we obtain the moment conditions for the supermun of normed sums of ρ~--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ~--mixing random variables. The result obtained generalize the results of Chen（2008） and extend those to negatively associated sequences and ρ~--mixing random variables.     

相依序列加权和的收敛性

本文在相依序列下考虑加权和的ａ．ｓ．收敛性和完全收敛性．所得结论推广并改进了［１］、［２］中有关结论．     

On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables

In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated（m-NA） random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.     

关于任意非负随机序列随机和的一类随机偏差定理

本文引入任意随机变量序列随机极限对数似然比概念,作为任意相依随机序列联合分布与其边缘乘积分布“不相似”性的一种度量,利用构造新的密度函数方法来建立几乎处处收敛的上鞅,在适当的条件下,给出了任意受控随机序列的一类随机偏差定理.     

重尾随机变量和的大偏差

This paper is a further investigation of large deviations for sums of random variables S_n=sum form i=1 to n X_i and S(t)=sum form i=1 to N(t) X_i,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.     

Complex Stable Sums of Complex Stable Random Variables

A definition of complex stable random variables is presented which includes earlier definitions as special cases. The class of complex stable random variables is characterized and is shown to be a subclass of the operator stable random variables. The exact conditions under which a sum of independent complex stable random variables is again complex stable are also found.