on random variables and their distributions

A Course in Mathematical Statistics

Ngày tải lên : 09/06/2015, 15:11

... Variables and Their Distributions 53 3.1 3.2 3.3 3.4 3.5* Chapter Some General Concepts 53 Discrete Random Variables (and Random Vectors) 55 Exercises 61 Continuous Random Variables (and Random Vectors) ... Distribution Function (c.d.f or d.f.) of a Random Vector—Basic Properties of the d.f of a Random Variable 85 Exercises 89 The d.f of a Random Vector and Its Properties—Marginal and Conditional d.f.’s and ... sections characteristic functions for the one-dimensional and the multidimensional case, and also by isolating in a section by itself deﬁnitions and results on momentgenerating functions and factorial...

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independent and stationary sequences of random variables

Ngày tải lên : 08/04/2014, 12:28

... Distributions and distribution functions 19 Convergence of distributions 21 Moments and characteristic functions 24 Continuity of the correspondence between distributions and characteristic functions ... (b) - F (a), and X (w) = w 21 CONVERGENCE OF DISTRIBUTIONS Let X and Y be independent random variables with respective distribution functions F1 and F2 The distribution function F of X + ... shows that only infinitely divisible distributions can arise as limits of distributions of sums of independent random variables Consider, for each n, a collection of independent random variables, ...

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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

... that the random variable X belongs to the domain of attraction of the normal law, if there exist constants an > 0, bn ∈ R such that S n − bn d −→ N, an where N is the standard normal random variable ... obtained by Lacey and Philipp [4], Ibragimov and Lifshits [5], Miao [6], Berkes and Cs´ ki [7], H¨ rmann [8], Wu [9, 10], and Ye and Wu [11] Huang and Zhang [12] and Zhang a o and Yang [13] obtained ... ) (14) (15) (16) where dk and Dn are deﬁned by (4) and f is a non-negative, bounded Lipschitz function Proof ¯ By the cental limit theorem for i.i.d random variables and VarS n ∼ nl(ηn ) as n...

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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

... Inequalities and Applications In addition, if inf ξ ≥ 0, one defines the geometric mean of the random variable ξ, G ξ , to be Gξ sup ξ· inf ξ 1.2 Definition 1.3 If ξ1 , , ξn are bounded random variables, ... 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 ξη G ξ, η 1.6 Equality holds if and only if P ξ η a B ... We define the random variable ζ, and assign P ζ λi ζβi /2 , i 1, , n Notice that λ1 and λn are the upper and lower bounds of the random variable ζ, so li and Li are the lower and upper bounds...

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Independent And Stationary Sequences Of Random Variables ppt

Ngày tải lên : 27/06/2014, 03:20

... (b) - F (a), and X (w) = w 21 CONVERGENCE OF DISTRIBUTIONS Let X and Y be independent random variables with respective distribution functions F1 and F2 The distribution function F of X + ... shows that only infinitely divisible distributions can arise as limits of distributions of sums of independent random variables Consider, for each n, a collection of independent random variables, ... and characteristic functions The correspondence between probability distributions on the real line and their characteristic functions is not only one-to-one, but also continuous in the following...

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