Stable Distributions. Models for Heavy Tailed Data

By J. L. Nolan. 2001

953 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1f4bcac0d87372add1364a4d1306e0bfc597fdd6

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Citations in the corpus

Affine Independent Variational Inference (2012, background): “The notable exception is the family of stable distributions for which linear combinations of random variables are also stable distributed (see [19] for an introduction).”
Portfolio Modeling with Heavy Tailed Random Vectors (2003, methodology): “Maximum likelihood estimation for the stable parameters is now practical, using the efficient method of Nolan [56] for computing stable densities, see also Mittnik, et al. [51, 52].”
Financial Risk and Heavy Tails (2003, methodology): “For an in depth introduction to the general properties of stable distributions see Samorodnitsky and Taqqu [ST94] and the upcoming text Nolan [Nol01].”
Expectile Asymptotics (2015, unknown): “Since yαP (I(µτ , Y ) > y) → τα c+ and yαP (I(µτ , Y ) −y) → (1− τ)α c− as y → ∞, this follows from the general CLT for distributions in the normal domain of attraction of a corresponding stable law (Nolan, 2015, p. 22).”
Are output growth-rate distributions fat-tailed? some evidence from OECD countries (2008, methodology): “Copyright 2008 John Wiley & Sons, Ltd. 1999; Nolan, 2006) and the Student-t.”
Pan-private algorithms via statistics on sketches (2011, background): “[15] A distribution S(p) over R is said to be p-stable if there exists p ≥ 0 such that for any n real numbers b1, .”
Models for Heavy-tailed Asset Returns (2010, background): “If only the finite variance assumption is released we have a straightforward solution by virtue of the generalized CLT, which states that the limiting distribution of sums of such variables is stable (Nolan, 2010).”
Modeling financial data with stable distributions (2003, background): “We give no proofs; interested readers can find these in Zolotarev (1983), Samorodnitsky and Taquu (1994), Janicki and Weron (1994), Uchaikin and Zolotarev (1999), Rachev and Mittnik (2000) and Nolan (2003).”
Boundary regularity for fully nonlinear integro-differential equations (2014, background): “Notice that the subsolution ϕ2 constructed above is C 1,1 by below in B1\B1/2, in the sense that it can be touched by below by paraboloids.”
Bibliography on stable distributions, processes and related topics (2004, background): “…(1998), Ilow (1999), Ilow and Hatzinakos (1997), Ilow and Hatzinakos (1998), Núñez et al. (2008), Nolan (2008), Gonzalez et al. (1997), Gonzalez and Nolan (2007), Wang et al. (2009b), Liu et al. (2008), Zha and Qiu (2007), Tsihrintzis and Nikias (1995), Zimmermann and Dostert (2002), Rupi et al.…”
Liouville quantum gravity as a mating of trees (2014, background): “It is well known in the literature on stable processes, that these properties imply that L1 is a Gaussian with mean zero [Nol03].”
Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression (2012, background): “Next, we state the following lemma, which is due to Nolan [27].”