Results 231 to 240 of about 31,371 (275)

On Geometric Infinite Divisibility and Stability

Annals of the Institute of Statistical Mathematics, 2000
The paper studies geometric infinite divisibility and geometric stability of distributions with support on the nonnegative integers \(\mathbb Z_+\) and the nonnegative reals \(\mathbb R_+\), respectively. Several new characterizations are obtained. It is shown that compound-geometric (resp.
Aly, Emad-Eldin A. A., Bouzar, Nadjib
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Infinitely Divisible Matrices

The American Mathematical Monthly, 2006
Assembling natural numbers in such nice patterns often has interesting consequences, and so it is in this case. Each of the aforementioned matrices is endowed with positive definiteness of a very high order: for every positive real number r the matrices with entries a\-, b\-, c\-, and d\are positive semidefinite.
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On the Infinite Divisibility of Polynomials in Infinitely Divisible Random Variables

1992
It is shown that all second degree polynomials in standard normal random variables are infinitely divisible and an example of a polynomial of degree three or more is given which is not infinitely divisible. It is also shown that if a polynomial in a random variable with support {0,1,2,…} is infinitely divisible then it must be linear.
V. K. Rohatgi, G. J. Székely
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Testing Max-Infinite Divisibility

Theory of Probability & Its Applications, 1993
See the review in Zbl 0753.62036.
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Convolution equivalence and infinite divisibility

Journal of Applied Probability, 2004
Known results relating the tail behaviour of a compound Poisson distribution function to that of its Lévy measure when one of them is convolution equivalent are extended to general infinitely divisible distributions. A tail equivalence result is obtained for random sum distributions in which the summands have a two-sided distribution.
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Infinitely divisible distributions in turbulence

Physical Review E, 1994
The imbedding of the scale similarity of random fields into the theory of infinitely divisible probability distributions is considered. The general probability distribution for the breakdown coefficients of turbulent energy dissipation is obtained along with corresponding similarity exponents.
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Max-infinite divisibility

Journal of Applied Probability, 1977
Necessary and sufficient conditions are given for a distribution function in ℝ2 to be max-infinitely divisible. The d.f. F is max i.d. if F t is a d.f. for every t > 0. This property is essential in defining multivariate extremal processes and arises in an approach to the study of the range of an i.i.d. sample.
Balkema, A. A., Resnick, S. I.
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Infinitely Divisible Distributions

2014
For every n, the normal distribution with expectation μ and variance σ 2 is the nth convolution power of a probability measure (namely of the normal distribution with expectation μ/n and variance σ 2/n). This property is called infinite divisibility and is shared by other probability distributions such as the Poisson distribution and the Gamma ...
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Infinitely Divisible Processes

2016
Infinitely divisible stochastic processes form a broad family whose structure is reasonably well understood. A stochastic process \({\bigl (X(t),\,t \in T\bigr )}\) is said to be infinitely divisible if for every n = 1, 2, …, there is a stochastic process \(\bigl( Y(t),\, t\in T\bigr)\) such ...
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