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COMPOUND RANDOM VARIABLES
"... We give a probabilistic proof of an identity concerning the expectation of an arbitrary function of a compound random variable and then use this identity to obtain recursive formulas for the probability mass function of compound random variables when the compounding distribution is Poisson, binomial ..."
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Cited by 10 (0 self)
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We give a probabilistic proof of an identity concerning the expectation of an arbitrary function of a compound random variable and then use this identity to obtain recursive formulas for the probability mass function of compound random variables when the compounding distribution is Poisson
Symmetrization Of Binary Random Variables
 BERNOULLI
, 1999
"... A random variable Y is called an independent symmetrizer of a given random variable X if (a) it is independent of X and (b) the distribution of X Y is symmetric about 0. In cases where the distribution of X is symmetric about its mean, it is easy to see that the constant random variable Y i ..."
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Cited by 2 (0 self)
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A random variable Y is called an independent symmetrizer of a given random variable X if (a) it is independent of X and (b) the distribution of X Y is symmetric about 0. In cases where the distribution of X is symmetric about its mean, it is easy to see that the constant random variable Y
Discrete Random Variables: Basics
"... • Given an experiment and the corresponding set of possible outcomes (the sample space), a random variable associates a particular number with each ..."
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• Given an experiment and the corresponding set of possible outcomes (the sample space), a random variable associates a particular number with each
Addition of freely independent Random variables
 J. Funct. Anal
, 1992
"... A direct proof is given of Voiculescu’s addition theorem for freely independent realvalued random variables, using resolvents of selfadjoint operators. In contrast to the original proof, no assumption is made on the existence of moments above the second. The concept of independent random variable ..."
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Cited by 62 (3 self)
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A direct proof is given of Voiculescu’s addition theorem for freely independent realvalued random variables, using resolvents of selfadjoint operators. In contrast to the original proof, no assumption is made on the existence of moments above the second. The concept of independent random
Discrete Stable Random Variables
 In 8th ICLP
, 1998
"... In Steutel and van Harn (1979) a discrete analogue of stability was introduced. In the present note we consider same explicit and asymptotic formulae for the probabilities and the tail of the distribution of discrete stable random variables and give rates for the convergence of sequences of certain ..."
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Cited by 5 (0 self)
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In Steutel and van Harn (1979) a discrete analogue of stability was introduced. In the present note we consider same explicit and asymptotic formulae for the probabilities and the tail of the distribution of discrete stable random variables and give rates for the convergence of sequences of certain
LognormalRice Random Variables
, 2006
"... A simple and novel method is presented to approximate by the lognormal distribution the probability density function of the sum of correlated lognormal random variables. The method is also shown to work well for approximating the distribution of the sum of lognormalRice or Suzuki random variables b ..."
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A simple and novel method is presented to approximate by the lognormal distribution the probability density function of the sum of correlated lognormal random variables. The method is also shown to work well for approximating the distribution of the sum of lognormalRice or Suzuki random variables
THE CONVEX ANALYSIS OF RANDOM VARIABLES
"... Any realvalued random variable induces a probability distribution on the real line which can be described by a cumulative distribution function. When the vertical gaps that may occur in the graph of that function are filled in, one gets a maximal monotone relation which describes the random variabl ..."
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Any realvalued random variable induces a probability distribution on the real line which can be described by a cumulative distribution function. When the vertical gaps that may occur in the graph of that function are filled in, one gets a maximal monotone relation which describes the random
ON THEORIES OF RANDOM VARIABLES
, 2009
"... We study theories of spaces of random variables: first, we consider random variables with values in the interval [0, 1], then with values in an arbitrary metric structure, generalising Keisler’s randomisation of classical structures. We prove preservation and nonpreservation results for model the ..."
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Cited by 4 (0 self)
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We study theories of spaces of random variables: first, we consider random variables with values in the interval [0, 1], then with values in an arbitrary metric structure, generalising Keisler’s randomisation of classical structures. We prove preservation and nonpreservation results for model
FUZZY RANDOM VARIABLES
"... Abstract. We outline the theory of Dposets of fuzzy sets and its applications to probability theory. In particular, we deal with generalizations of random variables. Key words and phrases. Dposet of fuzzy sets, fuzzy random variable, statistical map, random map. Mathematics Subject Classification. ..."
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Abstract. We outline the theory of Dposets of fuzzy sets and its applications to probability theory. In particular, we deal with generalizations of random variables. Key words and phrases. Dposet of fuzzy sets, fuzzy random variable, statistical map, random map. Mathematics Subject Classification
Random variables in a graph . . .
, 2005
"... In [15], we constructed a W ∗probability space (W ∗ (G), E) with amalgamation over a von Neumann algebra DG, where W ∗ (G) is a graph W ∗algebra induced by the countable directed graph G. In [15], we computed the DGvalued moments and cumulants of arbitrary random variables in (W ∗ (G), E) and we ..."
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Cited by 1 (1 self)
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In [15], we constructed a W ∗probability space (W ∗ (G), E) with amalgamation over a von Neumann algebra DG, where W ∗ (G) is a graph W ∗algebra induced by the countable directed graph G. In [15], we computed the DGvalued moments and cumulants of arbitrary random variables in (W ∗ (G), E
Results 11  20
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26,246