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Empirical Economics

Erschienen in:

28.09.2018

A review of Student’s t distribution and its generalizations

verfasst von: Rui Li, Saralees Nadarajah

Erschienen in: Empirical Economics | Ausgabe 3/2020

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Abstract

The Student’s t distribution is the most popular model for economic and financial data. In recent years, many generalizations of the Student’s t distribution have been proposed. This paper provides a review of generalizations, including software available for them. A real data application is presented to compare some of the reviewed distributions.

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Aas K, Haff IH (2006) The generalized hyperbolic skew Student’s \(t\) distribution. J Financ Econom 4:275–309CrossRef

Acitas S, Senoglu B, Arslan O (2015) Alpha-skew generalized \(t\) distribution. Rev Colomb Estad 38:353–370CrossRef

Ahsanullah M, Kibria BMG, Shakil M (2014) Normal and Student’s \(t\) distributions and their applications. Atlantis Press, Paris

Akahira M (1995) A higher order approximation to a percentage point of the non-central t-distribution. Commun Stat Simul Comput 24:595–605CrossRef

Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19:716–723CrossRef

Arnold BC, Beaver RJ (2002) Skewed multivariate models related to hidden truncation and/or selective reporting. Test 11:7–54CrossRef

Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Statist 12:171–178

Azzalini A, Capitanio A (2003) Statistical applications of the multivariate skew normal distribution. J R Stat Soc B 61:579–602CrossRef

Baker RD (2016) A new asymmetric generalisation of the \(t\) distribution. arXiv:1606.05203 [stat.ME]

Bergmann DR, de Oliveira MA (2013) Modeling the distribution of Brazilian Stock Returns via scaled Student \(t\). Int Res J Finance Econ 108:27–38

Brazauskas V, Kleefeld A (2011) Folded- and log-folded-\(t\) distributions as models for insurance loss data. Scand Actuar J 2011:59–74CrossRef

Burnham KP, Anderson DR (2004) Multimodel inference: understanding AIC and BIC in model selection. Sociol Methods Res 33:261–304CrossRef

Cademartori D, Romo C, Campos R, Galea M (2003) Robust estimation of systematic risk using the \(t\) distribution in the Chilean Stock Markets. Appl Econ Lett 10:447–453CrossRef

Cassidy DT, Hamp MJ, Ouyed R (2010) Pricing European options with a log Student’s \(t\) distribution: a Gosset formula. Phys A Stat Mech Appl 389:5736–5748CrossRef

Fang Y (2011) Asymptotic equivalence between cross-validations and Akaike Information Criteria in mixed-effects models. J Data Sci 9:15–21

Fernandez C, Steel MFJ (1998) On Bayesian modelling of fat tails and skewness. J Am Stat Assoc 93:359–371

Gómez HW, Torres FJ, Bolfarine H (2007a) Large-sample inference for the epsilon-skew-\(t\) distribution. Commun Stat Theory Methods 36:73–81CrossRef

Gómez HW, Varela H, Vidal L (2013) A new class of skew-symmetric distributions and related families. Statistics 47:411–421CrossRef

Gómez HW, Venegas O, Bolfarine H (2007b) Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics 18:395–407CrossRef

Gosset WS (1908) The probable error of a mean. Biometrika 6:1–25CrossRef

Harvey A, Lange R (2015) Volatility modelling with a generalized \(t\) distribution. Cambridge Working Papers in Economics, Faculty of Economics, Cambridge University

Hasan AM (2013) A study of non-central skew \(t\) distributions and their applications in data analysis and change point detection. Ph.D. Thesis, Bowling Green State University, OH, USA

Ho HJ, Pyne S, Lin TI (2012) Maximum likelihood inference for mixtures of skew Student-\(t\)-normal distributions through practical EM-type algorithms. Stat Comput 22:287–299CrossRef

Johnson NL, Kotz S, Balakrishnan N (1995) Continuous univariate distributions, vol 2, 2nd edn. Wiley, New York

Jones MC, Faddy MJ (2003) A skew extension of the \(t\) distribution, with applications. J R Stat Soc B 65:159–174CrossRef

Jones MC, Pewsey A (2009) Sinh-arcsinh distributions. Biometrika 96:761–780CrossRef

Kim H (2008) Moments of truncated Student-\(t\) distribution. J Korean Stat Soc 37:81–87CrossRef

Ku YHH (2008) Student-\(t\) distribution based VAR-MGARCH: an application of the DCC model on international portfolio risk management. Appl Econ 40:1685–1697CrossRef

Levy KJ, Narula SC (1974) Probability density plots of the non-central t-distribution. Int Stat Rev 42:305–306CrossRef

Li R, Nadarajah S (2016) The Kumaraswamy skew \(G\) distributions. Bull Braz Math Soc (submitted)

McDonald JB, Newey WK (1988) Partially adaptive estimation of regression models via the generalized \(t\) distribution. Econ Theory 4:428–457CrossRef

Mittnik S, Paolella MS (2000) Conditional density and Value-at-Risk prediction of Asian currency exchange rates. J Forecast 19:313–333CrossRef

Nadarajah S (2008) On the generalized \(t\) (GT) distribution. Statistics 42:467–473CrossRef

Ord JK (1968) The discrete Student’s \(t\) distribution. Ann Math Stat 39:1513–1516CrossRef

Paolella M (1997) Tail estimation and conditional modeling of heteroscedastic time series. Ph.D. thesis, Institute of Statistics and Econometrics, Christian Albrechts University at Kiel

Papastathopoulos I, Tawn JA (2013) A generalised Student’s \(t\)-distribution. Stat Probab Lett 83:70–77CrossRef

Psarakis S, Panaretos J (2007) The folded \(t\) distribution. Commun Stat Theory Methods 19:2717–2734CrossRef

R Development Core Team (2016) A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

Roozegar R, Nematollahi A, Jamalizadeh A (2016) Properties and inference for a new class of skew-\(t\) distributions. Commun Stat Simul Comput 45:3217–3237CrossRef

Rosco JF, Jones MC, Pewsey A (2011) Skew \(t\) distributions via the sinh-arcsinh transformation. Test 20:630–652CrossRef

Schlüter S, Fischer M (2012) A tail quantile approximation for the Student t distribution. Commun Stat Theory Methods 41:2617–2625CrossRef

Schwarz GE (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRef

Sepanski JH, Kong L (2007) A family of generalized beta distributions for income. arXiv:0710.4614v1

Shafiei S, Doostparast M (2014) Balakrishnan skew-\(t\) distribution and associated statistical characteristics. Commun Stat Theory Methods 43:4109–4122CrossRef

Shittu OI, Adepoju KA, Adeniji OE (2014) On beta skew-\(t\) distribution in modelling stock returns in Nigeria. Int J Mod Math Sci 11:94–102

Theodossiou P (1998) Financial data and the skewed generalized \(t\) distribution. Manag Sci 44:1650–1661CrossRef

Zhu D, Galbraith JW (2010) A generalized asymmetric Student-\(t\) distribution with application to financial econometrics. J Econ 157:297–305CrossRef

Titel: A review of Student’s t distribution and its generalizations
verfasst von: Rui Li
Saralees Nadarajah
Publikationsdatum: 28.09.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 3/2020
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-018-1570-0

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