Hidden regular variation and the rank transform

Heffernan, Janet E.; Resnick, Sidney I.

doi:10.1017/s0001867800000239

Cited by 18 publications

(16 citation statements)

References 29 publications

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“…For more details on characterizations and examples of HRV, see Resnick (2002), Maulik and Resnick (2004) and Heffernan and Resnick (2005). First, we define two cones:…”

Section: Preliminaries On Regular Variationmentioning

confidence: 99%

Second-order properties of tail probabilities of sums and randomly weighted sums

Mao

2015

Extremes

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Let X 1 , . . . , X n be independent nonnegative random variables with respective survival functions F 1 , . . . , F n , and let 1 , . . . , n be (not necessarily independent) nonnegative random variables, independent of X 1 , . . . , X n , satisfying certain moment conditions. This paper consists of two parts. In the first part, we investigate second-order expansions of P n i=1 X i > t as t → ∞ under the assumption that the F i are of second-order regular variation (2RV) with the same first-order index but with different second-order indexes. In the second part, under the assumption that the F 1 = · · · = F n have 2RV tails, second-order expansions of tail probabilities of the randomly weighted sum n i=1 i X i are studied. The closure property of 2RV under randomly weighted sum is also discussed. The main results in this paper generalize and strengthen several known results in the literature.

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“…For more details on characterizations and examples of HRV, see Resnick (2002), Maulik and Resnick (2004) and Heffernan and Resnick (2005). First, we define two cones:…”

Section: Preliminaries On Regular Variationmentioning

confidence: 99%

Second-order properties of tail probabilities of sums and randomly weighted sums

Mao

2015

Extremes

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“…Dependence and network models 63 Guerin et al (2003); Heffernan and Resnick (2005);Hernández-Campos et al (2005); Leland et al (1994); Maulik et al (2002); Park and Willinger (2000); Resnick (2003Resnick ( ), (2004aReidi and Willinger (2000); Sarvotham et al (2005);and Willinger et al (1995). With these assumptions, the counting function of the points…”

Section: Model Descriptionmentioning

confidence: 99%

The influence of dependence on data network models

D’Auria¹,

Resnick

2008

Adv. Appl. Probab.

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Consider an infinite-source marked Poisson process to model end user inputs to a data network. At Poisson times, connections are initated. The connection is characterized by a triple (F, L, R) denoting the total quantity of transmitted data in a connection, the length or duration of the connection, and the transmission rate; the three quantities are related by F = LR. How critical is the dependence structure of the mark for network characteristics such as burstiness, distribution tails of cumulative input, and longrange dependence properties of traffic measured in consecutive time slots? In a previous publication (D'Auria and Resnick (2006)) we assumed that F and R were independent. Here we assume that L and R are independent. The change in dependence assumptions means that the model properties change dramatically: tails of cumulative input per time slot are dramatically heavier, traffic cannot be approximated by a Gaussian distribution, and the decay of dependence cannot be measured in the traditional way using correlation functions. Different network applications are likely to have different mark dependence structure. We argue that the present independence assumption on L and R is likely to be appropriate for network applications such as streaming media or peer-to-peer networks. Our conclusion is that it is desirable to separate network traffic by application and to model each application with its own appropriate dependence structure.

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“…See Azzouna et al (2004), Campos et al (2005), Guerin et al (2003), Heffernan and Resnick (2005), Leland et al (1994), Maulik et al (2002), Park and Willinger (2000), Resnick (2003Resnick ( , 2004, Riedi and Willinger (2000), Sarvotham et al (2005), Willinger et al (1995).…”

Section: Model Descriptionmentioning

confidence: 99%

Data network models of burstiness

Auria¹,

Resnick

2006

Adv. Appl. Probab.

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Abstract. We review characteristics of data traffic which we term stylized facts: burstiness, long range dependence, heavy tails, bursty behavior determined by high bandwidth users, dependence determined by users without high transmission rates. We propose an infinite source Poisson input model which accounts for traffic in adjacent time slots. This model has the ability to account for many of the stylized facts.

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Hidden regular variation and the rank transform

Cited by 18 publications

References 29 publications

Second-order properties of tail probabilities of sums and randomly weighted sums

Second-order properties of tail probabilities of sums and randomly weighted sums

The influence of dependence on data network models

Data network models of burstiness

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