[PDF] Top 20 On the characteristic function of a sum of M dependent random variables

... RHEE Faculty of Management Sciences The Ohio State University Columbus, Ohio 43210... We will estimate the bound of.[r] ... See full document

... the characteristic function to tackle the problem of the sum of stochastic ...reduced variables are identically distributed, including those that violate the conditions for the central limit ... See full document

... WAN SOO RHEE Faculty of Management Sciences The Ohio State University Columbus, Ohio 43210.. of m-dependent random variables with..[r] ... See full document

... the sum of t and Gaussian random variables and pointed out its application in Bayesian wavelet ...of random variables associated with special ...of sum of several independent ... See full document

... the characteristic function of X and give an interpretation for the variable ...distribution function of X and prove some of its ...density function. In Section 5 distribution of sum of ... See full document

... To prove our main result, we'll need the following lemma. That provides some conditions under which the weighted sum converges completely and determinate the rate of convergence. The concept of complete ... See full document

... Moreover, they proved that the sequence of arithmetic means of independent identically distribution (i.i.d.) random variables converges completely to the expected value if the variance of the summands is ... See full document

... between random variables that we generated dependent Raeighly distribution using Archimedean copula and Kendall distribution ...distribution function is selected suitable copula ... See full document

... of random variables are not known and should be estimated based on historical ...number, m, of given scenarios for random variables and in the case of continuous variables we ... See full document

... Since the definition of complete convergence was introduced by Hsu and Robins, there have been many authors who devote themselves to the study of the complete convergence for sums of independent and dependent RVs ... See full document

... Lemma 3. Suppose that X 1 , , " X n , " are identically random variables with E X ( 1 ) 0 = and E X ( 1 p ) < ∞ for some p ∈ (0, 2) that satisfying in Marcinkiewicz and Zygmund’s theorem. Assume ... See full document

... = ∑ X n = S n ( ) / n . Landers and Rogge [8] proved a strong law of large numbers (SLLN) for pairwise independent and strongly uniformly integrable r.v.’s. Chandra and Goswami [3] proved a more general SLLN for pairwise ... See full document

... In this paper, we give a sufficient condition under which 1.2 and 1.3 hold. Our results partially improve those of Hu et al. 1, 2. The technique used in our proof is the well- known method of subsequences. Note that the ... See full document

... Robbins [] proved that the sequence of arithmetic means of independent and identi- cally distributed (i.i.d.) random variables converges completely to the expected value if the variance of the summands is ... See full document

... This paper will mainly focus on the asymptotic behavior of the tail probability of a weighted infinite sum of heavy-tailed r.v.s under the above two extended conditional de- pendence structures. In the rest of this ... See full document

... In this paper, we use different methods from those of Sung [] and Chen and Sung [] to prove the results, and we obtain some strong convergence results for weighted sums of NSD random variables without the ... See full document

... [19] C. Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, Proceedings of the Sixth Berkeley Symposium on Mathematical ... See full document

... In (.), a ≈ b means that a = O(b) and b = O(a). Theorem . extends the result of Liang and Su [] for negatively associated random variables to negatively dependent case. The proof of the ... See full document

... the random walk was ...for random walks is unacceptable for special class problems, since it is based on the use of distribution of one-boundary functionals, whereas for determining the latter, ... See full document

... In this paper, we generalize some results of Chandra and Goswami [4] for pairwise negatively dependent random variables (henceforth r.v.’s). Furthermore, we give Baum and Katz’s [1] type results on ... See full document