means of continuous random variables

theory and problems of probability, random variables, and random processes - hwei p. hsu

Ngày tải lên : 31/03/2014, 16:25

... Functions of One Random Variable 4.3 Functions of Two Random Variables 4.4 Functions of n Random Variables 4.5 Expectation 4.6 Moment Generating Functions 4.7 Characteristic Functions 4.8 The Laws of ... densityfunction (pdf) of the continuous r.v X RANDOM VARIABLES Properties of fx(x) : fx(x) is piecewise continuous The cdf FX(x )of a continuous r.v X can be obtained by By Eq (2.19),if X is a continuous ... Schaum's Outline of Theory and Problems of Probability, Random Variables, and Random Processes Hwei P Hsu, Ph.D Professor of Electrical Engineering Fairleigh Dickinson University Start of Citation[PU]McGraw-Hill...

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Báo cáo hóa học: " A note on the complete convergence for arrays of dependent random variables" docx

Ngày tải lên : 20/06/2014, 22:20

... convergence results for independent random variables have been extended to dependent random variables by many authors The concept of negatively associated random variables was introduced by Alam ... version of Theorem 1.2 for negatively dependent random variables Theorem 1.6 Let {Xni, ≤ i ≤ kn, n ≥ 1} be an array of rowwise negatively dependent random variables and {an, n ≥ 1} a sequence of nonnegative ... exists An infinite family of random variables is negatively associated if every finite subfamily is negatively associated The concept of negatively dependent random variables was introduced by...

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báo cáo hóa học:" Research Article ¨ Gruss-Type Bounds for the Covariance of Transformed Random Variables" potx

Ngày tải lên : 21/06/2014, 18:20

... for the covariance of two transformed random variables by incorporating a notion of quadrant dependence and also utilizing the idea of constraining the means of the random variables To see how ... sharpens the upper bound of Gruss’s covariance inequality ¨ 3.3 by utilizing the notion of quadrant dependence cf Lehmann 12 and incorporating constrains on the means of random variables X and Y cf ... 2.4 Journal of Inequalities and Applications Approaching the problem from a diﬀerent angle, Zitikis has sharpened Gruss’s ¨ bound by including restrictions on the means of the random variables...

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Báo cáo hóa học: "HAJEK-RENYI-TYPE INEQUALITY FOR SOME NONMONOTONIC FUNCTIONS OF ASSOCIATED RANDOM VARIABLES" potx

Ngày tải lên : 22/06/2014, 22:20

... nonmonotonic functions of associated random variables in Section As an application, a strong law of large numbers is derived for nonmonotonic functions of associated random variables in Section ... numbers for nonmonotonic functions of associated random variables Corollary 4.2 Let {Yn , n ≥ 1} be sequence of nonmonotonic functions of associated random variables satisfying the conditions ... of the three series theorem for nonmonotonic functions of associated random variables Corollary 4.4 Let {Yn , n ≥ 1} be sequence of nonmonotonic functions of associated rank k Yn satisfydom variables...

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Báo cáo "On the stability of the distribution function of the composed random variables by their index random variable " pdf

Ngày tải lên : 14/03/2014, 13:20

... occasion of 50th Anniversary of Department of Mathematics, Mechanics and Informatics, Vietnam National University References [1] Tran Kim Thanh, On the characterization of the distribution of the ... composed random variables and their stabilities Dotor thesis, Hanoi 2000 [2] Tran Kim Thanh, Nguyen Huu Bao, On the geometric composed variables and the estimate of the stable degree of the Renyi’s ... )|t| = C|t| (1 − |ϕ(t) − 1|) (do |ϕ(t) − 1| µF |t| ∀t) where C is a constant independent of ε and µF = Proof of Theorem 2.1 +∞ −∞ |x|dF (x) < ∞ For every N > and t ∈ R1, we have +∞ |ψ(t) − ψ1 (t)|...

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independent and stationary sequences of random variables

Ngày tải lên : 08/04/2014, 12:28

... 10 Completion of the proof of sufficiency 240 11 Proof of the necessity 241 12 Completion of the proof 243 Chapter 13 Monomial zones of integral attraction to Cramer's system of limiting tails ... 171 Statement of the theorem The introduction of auxiliary random variables 172 Proof of the theorem 174 Chapter Monomial zones of local normal attraction 177 177 178 180 Zones of normal attraction ... the Borel sets of R" is the distribution of X, or the joint distribution of the variables X1 , X2 , , X,, More generally, if T is any set of real numbers, a family of random variables X (t),...

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Báo cáo toán học: " A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law" pptx

Ngày tải lên : 20/06/2014, 21:20

... sums of random variables in the domain of attraction of the normal law Qunying Wu1,2 College of Science, Guilin University of Technology, Guilin 541004, P R China Guangxi Key Laboratory of Spatial ... < ε0 < in theorem 1.1 of [12] Remark 1.4 If EX < ∞, then X is in the domain of attraction of the normal law Therefore, the class of random variables in Theorems 1.1 is of very broad range Remark ... sequence remains unknown The purpose of this article is to study and establish the ASCLT for self-normalized partial sums of random variables in the domain of attraction of the normal law, we will show...

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Báo cáo hóa học: " A note on the complete convergence for sequences of pairwise NQD random variables" potx

Ngày tải lên : 20/06/2014, 22:20

... almost sure convergence of summation of random variables Hsu and Robbins [8] proved that the sequence of arithmetic means of independent and identically distributed random variables converges completely ... the corresponding results of independent random variable sequences, there still remains much to be desired The concept of complete convergence of a sequence of random variables was introduced ... readability of the article Author details School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 610054, PR China College of Science, Guilin University of Technology,...

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Báo cáo hóa học: " Some strong limit theorems for arrays of rowwise negatively orthant-dependent random variables Aiting Shen" pptx

Ngày tải lên : 20/06/2014, 22:20

... is NOD An array of random variables {Xni, i ≥ 1, n ≥ 1} is called rowwise NOD random variables if for every n ≥ 1, {Xni, i ≥ 1} is a sequence of NOD random variables The concept of NOD sequence ... strong law of large numbers for arrays of rowwise NOD random variables Corollary 2.5 Let {Xni, i ≥ 1, n ≥ 1} be an array of rowwise NOD random variables and {an, n ≥ 1} be a sequence of positive ... purpose of this article is to study the strong limit theorems for arrays of rowwise NOD random variables As an application, the Chung-type strong law of large numbers for arrays of rowwise NOD random...

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Báo cáo hóa học: " Research Article Almost Sure Central Limit Theorem for Product of Partial Sums of Strongly Mixing Random Variables" docx

Ngày tải lên : 21/06/2014, 05:20

... Journal of Inequalities and Applications Lemma 2.4 see Let {ξk , k ≥ 1} be a sequence of random variables, uniformly bounded below and with ﬁnite variances, and let {dk , k ≥ 1} be a sequence of ... mixing sequence of random variables with zero mean and supn E|Xn |2 δ < ∞ for a certain δ > Assume that 1.5 and 1.6 hold Then lim sup n→∞ |Sn | 2σ0 n ln ln n a.s 2.9 2.2 Proof of Theorem 1.4 From ... 2004 J S Jin, “An almost sure central limit theorem for the product of partial sums of strongly missing random variables, ” Journal of Zhejiang University, vol 34, no 1, pp 24–27, 2007 I Berkes and...

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Báo cáo hóa học: " Research Article A Strong Limit Theorem for Weighted Sums of Sequences of Negatively Dependent Random Variables" potx

Ngày tải lên : 21/06/2014, 07:20

... weaker than NA Because of the wide applications of ND random variables, the notions of ND dependence of random variables have received more and more attention recently A series of useful results have ... Journal of Inequalities and Applications variables Consequently, the following definition is needed to define sequences of negatively dependent random variables Definition 1.2 The random variables ... properties of independent or NA random variables to the case of ND variables is highly desirable and of considerably significance in the theory and application Strong convergence is one of the most...

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Báo cáo hóa học: " Research Article On Complete Convergence for Arrays of Rowwise ρ-Mixing Random Variables and Its Applications" pdf

Ngày tải lên : 21/06/2014, 07:20

... ρ-mixing sequences of random variables, ” Chinese Annals of Mathematics Series A, vol 9, no 4, pp 409–412, 1988 Q M Shao, “On the invariance principle for ρ-mixing sequences of random variables, ” Chinese ... respectively, not −q/t in Theorem 2.1 of Kuczmaszewska 17 Now, we give the proof of Theorem 2.1 4 Journal of Inequalities and Applications Proof The conclusion of the theorem is obvious if consider ... array of rowwise ρ-mixing random variables satisfying 2/q supn ∞1 ρn 2i < ∞ for some q ≥ and EXni for all n ≥ 1, i ≥ Let the random variables in i each row be stochastically dominated by a random...

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Báo cáo hóa học: "Research Article Recurring Mean Inequality of Random Variables" doc

Ngày tải lên : 22/06/2014, 02:20

... Definition 1.4 If ξ1 , , ξn are bounded random variables with inf ξi ≥ 0, i 1, , n, one defines the independent geometric mean of the product of random variables ξ1 , , ξn to be n G ξ1 , ... ξ· inf ξ 1.2 Definition 1.3 If ξ1 , , ξn are bounded random variables, the independent arithmetic mean of the product of random variables ξ1 , , ξn , A ξ1 , , ξn is given by n i n sup ... ξn n A ξi , i G ξ1 , , ξn n G 1.5 ξi i The mean inequality of two random variables Theorem 1.6 Let ξ and η be bounded random variables If inf ξ > and inf η > 0, then Eξ ·Eη2 A ξ, η ≤ E2...

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Báo cáo hóa học: " Research Article Summability of Double Independent Random Variables potx

Ngày tải lên : 22/06/2014, 03:20

... term Thus p1 of the k s φθ1 , q1 of the k s ϕ1 , , qθ2 of the k s ϕθ2 , r1 of the l s κ1 , , rτ1 of the l s κτ1 , s1 of the l s where ≤ pi ≤ φ1 , , pθ1 of the k s ω1 , , sτ2 of the l ... limit inferior of x is deﬁned as −∞ for each n, then P-lim inf x : −∞; if βn > −∞ for some n, then P-lim inf x : supn {βn } Main result The analysis of double sequences of random variables via ... theorems,” International Journal of Mathematics and Mathematical Sciences, vol 22, no 4, pp 785–793, 1999 W E Pruitt, “Summability of independent random variables, ” Journal of Mathematics and Mechanics,...

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Independent And Stationary Sequences Of Random Variables ppt

Ngày tải lên : 27/06/2014, 03:20

... limiting distributions of normed sums Zn= Xl+X2+ + Xn _ An Bn (2.1 3) of stationarily dependent random variables In this section we establish this result for independent random variables ; the general ... X2+ + Xn of independent random variables with distribution F has distribution function of the form F (a n x + b n), so that X1 + +Xn _ an On has distribution function F The proof of the final ... form of the characteristic functions of stable laws The bulk of the chapter is devoted to the investigation of the analytical properties of the corresponding densities, which are by no means...

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