Titlebook: Closure Properties for Heavy-Tailed and Related Distributions; An Overview Remigijus Leipus,Jonas Šiaulys,Dimitrios Konstanti Book 2023 The

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Was verursacht Schizophrenien?,ons is caused by the inclusion of . to the same family. Such an implication is called a convolution-root closure. This chapter is devoted to the convolution-root closure properties for the distribution classes described in Chap. .. We determine the classes which are closed under convolution roots an

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https://doi.org/10.1007/978-3-540-75259-2This concluding chapter collects the closure properties for the heavy-tailed and related distribution classes, considered in the book. In order to see the whole picture for the validity of closure properties among the classes and compare them between themselves, we place them in Table 6.1.

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Summary of Closure Properties,This concluding chapter collects the closure properties for the heavy-tailed and related distribution classes, considered in the book. In order to see the whole picture for the validity of closure properties among the classes and compare them between themselves, we place them in Table 6.1.

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Introduction,n finance and insurance, communication networks, physics, hydrology, etc. Heavy-tailed distributions, whose most popular subclass is a class of regularly varying distributions, are also standard in applied probability when describing claim sizes in insurance mathematics, service times in queueing th

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Closure Properties Under Tail-Equivalence, Convolution, Finite Mixing, Maximum, and Minimum,s. In Sect. 3.3, we discuss the convolution closure properties in relation to the notion of max-sum equivalence. In further sections, we overview and discuss the closure properties of the heavy-tailed and related distributions, introduced in Chap. ., under strong/weak tail-equivalence, convolution,

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Convolution-Root Closure,ons is caused by the inclusion of . to the same family. Such an implication is called a convolution-root closure. This chapter is devoted to the convolution-root closure properties for the distribution classes described in Chap. .. We determine the classes which are closed under convolution roots an

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Product-Convolution of Heavy-Tailed and Related Distributions,blems, such as multivariate statistical modelling, asymptotic analysis of randomly weighted sums, etc. In financial time series, the multiplicative structures occur in modelling conditional heteroskedasticity as in GARCH or stochastic volatility models. In this chapter, we mainly are interested in t

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Introduction, not only an interesting mathematical problem. Using closure properties of a given distribution class, one can effectively construct the representatives of the class and understand the mechanisms causing heavy tails in real life.