Weak convergence to the Student and Laplace distributions

One often observed empirical regularity is a power-law behavior of the tails of some distribution of interest. We propose a limit law for normalized random means that exhibits such heavy tails irrespective of the distribution of the underlying sampling units: the limit is a t-distribution if the ran...
Ausführliche Beschreibung

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Autor*in:	Christian Schluter [verfasserIn] Mark Trede

Format:	Artikel
Sprache:	Englisch

Erschienen:	2016

Rechteinformationen:	Nutzungsrecht: © Copyright 2016 Applied Probability Trust

Schlagwörter:	Random number sampling Rates of return Probability distribution Growth models Theorems Studies Laplace transforms high-frequency return process 91B30 Limit theorem 60F05 city-size growth 62E20 91B70

Systematik:	SA 6100

Übergeordnetes Werk:	Enthalten in: Journal of applied probability - Cambridge : Cambridge University Press, 1964, 53(2016), 1, Seite 121-129
Übergeordnetes Werk:	volume:53 ; year:2016 ; number:1 ; pages:121-129

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Katalog-ID:	OLC197278076X

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520			\|a One often observed empirical regularity is a power-law behavior of the tails of some distribution of interest. We propose a limit law for normalized random means that exhibits such heavy tails irrespective of the distribution of the underlying sampling units: the limit is a t-distribution if the random variables have finite variances. The generative scheme is then extended to encompass classic limit theorems for random sums. The resulting unifying framework has wide empirical applicability which we illustrate by considering two empirical regularities in two different fields. First, we turn to urban geography and explain why city-size growth rates are approximately t-distributed, using a model of random sector growth based on the central place theory. Second, turning to an issue in finance, we show that high-frequency stock index returns can be modeled as a generalized asymmetric Laplace process. These empirical illustrations elucidate the situations in which heavy tails can arise.
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allfieldsSound	PQ20160430 (DE-627)OLC197278076X (DE-599)GBVOLC197278076X (PRQ)p1146-e72195545edb27d6d805582e7366b830bcb93919fbfcff847d6e11df60c542540 (KEY)0054615120160000053000100121weakconvergencetothestudentandlaplacedistributions DE-627 ger DE-627 rakwb eng 510 DNB SA 6100 AVZ rvk 31.70 bkl Christian Schluter verfasserin aut Weak convergence to the Student and Laplace distributions 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier One often observed empirical regularity is a power-law behavior of the tails of some distribution of interest. We propose a limit law for normalized random means that exhibits such heavy tails irrespective of the distribution of the underlying sampling units: the limit is a t-distribution if the random variables have finite variances. The generative scheme is then extended to encompass classic limit theorems for random sums. The resulting unifying framework has wide empirical applicability which we illustrate by considering two empirical regularities in two different fields. First, we turn to urban geography and explain why city-size growth rates are approximately t-distributed, using a model of random sector growth based on the central place theory. Second, turning to an issue in finance, we show that high-frequency stock index returns can be modeled as a generalized asymmetric Laplace process. These empirical illustrations elucidate the situations in which heavy tails can arise. Nutzungsrecht: © Copyright 2016 Applied Probability Trust Random number sampling Rates of return Probability distribution Growth models Theorems Studies Laplace transforms high-frequency return process 91B30 Limit theorem 60F05 city-size growth 62E20 91B70 Mark Trede oth Enthalten in Journal of applied probability Cambridge : Cambridge University Press, 1964 53(2016), 1, Seite 121-129 (DE-627)129549797 (DE-600)219147-7 (DE-576)015003027 0021-9002 nnns volume:53 year:2016 number:1 pages:121-129 http://search.proquest.com/docview/1775220986 http://projecteuclid.org/euclid.jap/1457470563 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_70 GBV_ILN_105 GBV_ILN_130 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2012 GBV_ILN_2015 GBV_ILN_2021 GBV_ILN_2088 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4125 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4311 GBV_ILN_4318 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 SA 6100 31.70 AVZ AR 53 2016 1 121-129
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author	Christian Schluter
spellingShingle	Christian Schluter ddc 510 rvk SA 6100 bkl 31.70 misc Random number sampling misc Rates of return misc Probability distribution misc Growth models misc Theorems misc Studies misc Laplace transforms misc high-frequency return process misc 91B30 misc Limit theorem misc 60F05 misc city-size growth misc 62E20 misc 91B70 Weak convergence to the Student and Laplace distributions
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topic_title	510 DNB SA 6100 AVZ rvk 31.70 bkl Weak convergence to the Student and Laplace distributions Random number sampling Rates of return Probability distribution Growth models Theorems Studies Laplace transforms high-frequency return process 91B30 Limit theorem 60F05 city-size growth 62E20 91B70
topic	ddc 510 rvk SA 6100 bkl 31.70 misc Random number sampling misc Rates of return misc Probability distribution misc Growth models misc Theorems misc Studies misc Laplace transforms misc high-frequency return process misc 91B30 misc Limit theorem misc 60F05 misc city-size growth misc 62E20 misc 91B70
topic_unstemmed	ddc 510 rvk SA 6100 bkl 31.70 misc Random number sampling misc Rates of return misc Probability distribution misc Growth models misc Theorems misc Studies misc Laplace transforms misc high-frequency return process misc 91B30 misc Limit theorem misc 60F05 misc city-size growth misc 62E20 misc 91B70
topic_browse	ddc 510 rvk SA 6100 bkl 31.70 misc Random number sampling misc Rates of return misc Probability distribution misc Growth models misc Theorems misc Studies misc Laplace transforms misc high-frequency return process misc 91B30 misc Limit theorem misc 60F05 misc city-size growth misc 62E20 misc 91B70
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title	Weak convergence to the Student and Laplace distributions
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title_full	Weak convergence to the Student and Laplace distributions
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title_sort	weak convergence to the student and laplace distributions
title_auth	Weak convergence to the Student and Laplace distributions
abstract	One often observed empirical regularity is a power-law behavior of the tails of some distribution of interest. We propose a limit law for normalized random means that exhibits such heavy tails irrespective of the distribution of the underlying sampling units: the limit is a t-distribution if the random variables have finite variances. The generative scheme is then extended to encompass classic limit theorems for random sums. The resulting unifying framework has wide empirical applicability which we illustrate by considering two empirical regularities in two different fields. First, we turn to urban geography and explain why city-size growth rates are approximately t-distributed, using a model of random sector growth based on the central place theory. Second, turning to an issue in finance, we show that high-frequency stock index returns can be modeled as a generalized asymmetric Laplace process. These empirical illustrations elucidate the situations in which heavy tails can arise.
abstractGer	One often observed empirical regularity is a power-law behavior of the tails of some distribution of interest. We propose a limit law for normalized random means that exhibits such heavy tails irrespective of the distribution of the underlying sampling units: the limit is a t-distribution if the random variables have finite variances. The generative scheme is then extended to encompass classic limit theorems for random sums. The resulting unifying framework has wide empirical applicability which we illustrate by considering two empirical regularities in two different fields. First, we turn to urban geography and explain why city-size growth rates are approximately t-distributed, using a model of random sector growth based on the central place theory. Second, turning to an issue in finance, we show that high-frequency stock index returns can be modeled as a generalized asymmetric Laplace process. These empirical illustrations elucidate the situations in which heavy tails can arise.
abstract_unstemmed	One often observed empirical regularity is a power-law behavior of the tails of some distribution of interest. We propose a limit law for normalized random means that exhibits such heavy tails irrespective of the distribution of the underlying sampling units: the limit is a t-distribution if the random variables have finite variances. The generative scheme is then extended to encompass classic limit theorems for random sums. The resulting unifying framework has wide empirical applicability which we illustrate by considering two empirical regularities in two different fields. First, we turn to urban geography and explain why city-size growth rates are approximately t-distributed, using a model of random sector growth based on the central place theory. Second, turning to an issue in finance, we show that high-frequency stock index returns can be modeled as a generalized asymmetric Laplace process. These empirical illustrations elucidate the situations in which heavy tails can arise.
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title_short	Weak convergence to the Student and Laplace distributions
url	http://search.proquest.com/docview/1775220986 http://projecteuclid.org/euclid.jap/1457470563
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