## Download PDF by Ashot Vazrikievich Kakosyan, Leo Borisovich Klebanov, Joseph: Characterization of Distributions by the Method of

By Ashot Vazrikievich Kakosyan, Leo Borisovich Klebanov, Joseph Aleksandrovich Melamed (auth.)

ISBN-10: 3540138579

ISBN-13: 9783540138570

ISBN-10: 3540390502

ISBN-13: 9783540390503

**Read or Download Characterization of Distributions by the Method of Intensively Monotone Operators PDF**

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**Extra resources for Characterization of Distributions by the Method of Intensively Monotone Operators**

**Example text**

F. ~ C~) of the random variable Xj random variable real ~ C j = 4 , ~ , .... f. , & & (~C0,~) is a constant). j=4 If statistes X e and ~ j=t Xj are identically distributed and there exists a finite limit & 6~ C4-~0Ct))/Itl, t-~O then the variable Xo is distributed law w i t h e x p o n e n t & , Proof. 's, has the form of I0 ct)= n ~; ct). 1) 35 Since n ~ laj Ct) l and I~j = Itl J~iC~) ( J = O , ~ ~ . . , ~) are non-degenerate c . f . 1) that otion ~o Ct) the fun- does not vanish on the real line.

1) coincides with function . 2) for are has the Laplace distribution. 0 The Laplace distribution may emerge as a limit one in the scheme of summation of a random amount of variables, as the parameter p-~0 (ice. as the average number of terms increases to infinity). 2. X~, ... be independent distributed symmetric random variables with ~ that the variables geometric and have a finite variance random variable, P{V=K} = ~(4-~) P{ independent , ~ ~(t) . Assume . f. identically "= F(S6) ~,roo~. f. of the sum i~pCt,)=~pC,I-p) )~ Xj p'/~_ J=4 function.

X ~ , (~4, ~ , ''''~ ~ °'') ... are independent random variables and is a random sequence, then the linear form CO z:, jx i with random coefficients ~i may be considered as a sum of conditioc~O nally independent variables ~ ~i J=4 , where characterization of the normal distribution ~ = ~j Xj - Thus, by the property of iden- tical distribution of a monomial and a linear form with random coefficients is a special case of the problem on identical distribution of a monomial and the sum of conditionally independent random variables.

### Characterization of Distributions by the Method of Intensively Monotone Operators by Ashot Vazrikievich Kakosyan, Leo Borisovich Klebanov, Joseph Aleksandrovich Melamed (auth.)

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