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On the sum of and Gaussian random variables
Statistics & Probability Letters, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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FLUCTUATIONS OF SUMS OF INDEPENDENT RANDOM VARIABLES
The Annals of Mathematics, 19501. One aspect of the theory of addition of independent random variables is the frequency with which the partial sums change sign. Investigations of this nature were originated by Paul L6vy, in a paper [1] which contains a wealth of ideas. This problem as such was mentioned by Feller in his 1945 address [2].
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On the Sum of Random Variables
1989In “statistics”, an experiment yields outcomes x1x2x3…; a common model is that these are observed values of random variables X1X2X3…. As in the simple cases of testing and estimation in Part I, what becomes meaningful are functions of the observations; such (measurable) functions are calledstatistics.One of the most commonly used functions is the ...
Hung T. Nguyen, Gerald S. Rogers
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2002
The command “Let X be …” empowers the mathematical modeller. The use of a single symbol X to represent the main object of interest, and the use of good notation in an analysis, are often a long stride towards the solution. In modelling random phenomena, we may find that X is either naturally the sum of other quantities Y 1,Y 2,…,Y n , or can be ...
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The command “Let X be …” empowers the mathematical modeller. The use of a single symbol X to represent the main object of interest, and the use of good notation in an analysis, are often a long stride towards the solution. In modelling random phenomena, we may find that X is either naturally the sum of other quantities Y 1,Y 2,…,Y n , or can be ...
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2020
In this chapter we examine the first-order statistical properties of the amplitude and phase of various kinds of random phasor sums. By “first-order” we mean the statistical properties at a point in space or, for time-varying speckle, in space–time.
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In this chapter we examine the first-order statistical properties of the amplitude and phase of various kinds of random phasor sums. By “first-order” we mean the statistical properties at a point in space or, for time-varying speckle, in space–time.
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Random Sums of Random Variables and Vectors [PDF]
, 2009 Let fX;Xi; i = 1; 2; :::g denote independent positive random variables having a common distribution function F(x) and, independent of X, let N denote an integer valued random variable. Using S(0) = 0 and S(n) = S(n ?? 1) + Xn, the random sum S(N) has distribution function G(x) = 1Xi=0 P(N = i)P(S(i) _ x) and tail distribution G(x) = 1 ?? G(x). In which
Omey, Edward, Vesilo, R.
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Sums of a Random Number of Random Variables
1995We consider a family of random variables \(\left\{ {\xi _i^n,\,i,\,n \in N} \right\},\,N = \left\{ {1,2, \ldots } \right\},\)defined on a probability space {Ω, F, P} and a family \(\left\{ {F_i^n,\,i \in {N_O},\,n \in N} \right\},\,{N_O} = \left\{ 0 \right\}U\)of sub σ-algebras of F such that E i n is F i n - measurable and \(F_i^n \subseteq F_{i + 1 ...
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