The Distribution of Sums of Certain I.I.D. Pareto Variates

Ramsay, Colin M.

doi:10.1080/03610920500476325

Cited by 50 publications

(28 citation statements)

References 8 publications

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“…It turns out that G P (x,α) behaves as the normal distribution for x < C, where C is a finite positive constant but features a heavy tail with the same exponent as u 1 (k) when x → ∞; see Ref. [30]. Thus, when θ 0 the component size distribution features asymptotic modes as in Eq.…”

Section: (18) No General Analytical Expression Is Known For Gmentioning

confidence: 94%

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General expression for the component size distribution in infinite configuration networks

Kryven

2017

Phys. Rev. E

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In the infinite configuration network the links between nodes are assigned randomly with the only restriction that the degree distribution has to match a predefined function. This work presents a simple equation that gives for an arbitrary degree distribution the corresponding size distribution of connected components. This equation is suitable for fast and stable numerical computations up to the machine precision. The analytical analysis reveals that the asymptote of the component size distribution is completely defined by only a few parameters of the degree distribution: the first three moments, scale, and exponent (if applicable). When the degree distribution features a heavy tail, multiple asymptotic modes are observed in the component size distribution that, in turn, may or may not feature a heavy tail.

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Section: (18) No General Analytical Expression Is Known For Gmentioning

confidence: 94%

“…This is indeed the case for x(n) ≈ 0. However, large deviations from zero x(n) 0 do not follow Gaussian statistics [30,31], and we approximate u * n 1 (k) with the Pareto stable law u * n…”

Section: (18) No General Analytical Expression Is Known For Gmentioning

confidence: 99%

General expression for the component size distribution in infinite configuration networks

Kryven

2017

Phys. Rev. E

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“…Chesneau [12], and Ramsay [74]. A recent work by Zaliapin [103] provides five approximation techniques for the Pareto sums and discusses their respective accuracy.…”

Section: On the Pareto Distribution Representing Rainfall Entropy Aggmentioning

confidence: 99%

Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes

Poveda

2011

Advances in Water Resources

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“…y * h y (x), for j ≥ 2, (it will be fast, k being small) and h 1 * y = h y , or, if α ∈ N * , the explicit expression (12) (replacing β by y) given in Ramsay (2006).…”

Section: A Conditional Decompositionmentioning

confidence: 99%

Normex, a new method for evaluating the distribution of aggregated heavy tailed risks

Kratz

2014

Extremes

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We develop theoretically as well as numerically a new method, Normex, for the sum of independent heavy tailed distributed random variables, to obtain the most accurate evaluation of its entire distribution. Normex provides sharp results, whatever the number of summands and the tail index are. It is particularly suited when the Central Limit Theorem (CLT) applies but with slow convergence of the mean and with a poor approximation for the tail. Hence, it is filling up a gap in the literature by giving an appropriate limit distribution in this case, in general better than with most standard methods. An application is developed to evaluate the Value-atRisk of the yearly log returns of financial assets. AMS 2000 Subject ClassificationsMarie Kratz is also member of MAP5, UMR 8145, Univ. Paris Descartes,

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The Distribution of Sums of Certain I.I.D. Pareto Variates

Cited by 50 publications

References 8 publications

General expression for the component size distribution in infinite configuration networks

General expression for the component size distribution in infinite configuration networks

Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes

Normex, a new method for evaluating the distribution of aggregated heavy tailed risks

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