A generalization of the beta distribution with applications

McDonald, James B.; Xu, Yexiao

doi:10.1016/0304-4076(94)01612-4

Cited by 406 publications

(208 citation statements)

References 12 publications

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“…This model is similar in spirit to the generalised skew student or GST distribution, which has been applied to returns on financial assets by several authors, including for example McDonald and Newey(1988), McDonald and Nelson(1989), McDonald and Xu(1995), Theodossiou(1998) and Harris et al(2004). The GED distribution arises as a special case of the GST as the parameter, which is analogous to degrees of freedom, tends to infinity.…”

Section: Ged-3 In Which All Parameters Are Unrestrictedmentioning

confidence: 96%

“…Several authors have used the generalised skew student or GST distribution to model returns on financial assets. Examples are studies by McDonald and Newey(1988), McDonald and Nelson(1989), McDonald and Xu(1995), Theodossiou(1998) and Harris et al(2004). Fielitz and Smith(1972) and Fielitz(1976) use asymmetric variants of the stable distribution.…”

Section: Literature Reviewmentioning

confidence: 99%

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An analysis of skewness and skewness persistence in three emerging markets

Adcock

Shutes

2005

Emerging Markets Review

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This paper reports an investigation into the extent and persistence of skewness in stock returns in three emerging markets, namely The Czech Republic, Kenya and Poland. Thee study is undertaken using the extended skew normal distribution and an asymmetric version of the generalised error distribution. The motivation for this paper is the hypothesis that skewness is a particular feature of returns in emerging markets; it may lack persistence and may decline in absolute terms as time passes and the market matures. When daily returns are considered, the majority of stocks in all three markets exhibit a significant degree of skewness. The value of the skewness parameter is often different in each of the three estimation periods considered. Little evidence has been found to support the view that skewness is an artifact of emerging or evolving markets. Over the period covered by the study, the number of stocks with a significant degree of skewness has remained more or less the same. For weekly returns, the same conclusions apply to The Czech Republic and to Kenya, but there is far less evidence of skewness in weekly returns on Polish Stocks.

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Section: Ged-3 In Which All Parameters Are Unrestrictedmentioning

confidence: 96%

Section: Literature Reviewmentioning

confidence: 99%

An analysis of skewness and skewness persistence in three emerging markets

Adcock

Shutes

2005

Emerging Markets Review

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“…These include Champernowne (1953), Singh and Maddala (1976), Dagum (1977), Kloek and van Dijk (1978), McDonald and Ransom (1979), van Dijk and Kloek (1980), McDonald (1984), Esteban (1986), Majumder and Chakravarty (1990), McDonald and Mantrala (1995), McDonald and Xu (1995), Bordley et al (1996), Parker (1999), Bandourian et al (2002) and Chotikapanich (2008). The distributions proposed include the log-normal distribution, the Gamma and Generalized Gamma distributions, the Burr 3 and Burr 12 distributions, and the GB1 and GB2 distributions.…”

Section: Introductionmentioning

confidence: 99%

Is the Pareto–Lévy law a good representation of income distributions?

Dagsvik

Jia

Vatne³

et al. 2011

Empir Econ

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Mandelbrot (1960) proposed using the so-called Pareto-Lévy class of distributions as a framework for representing income distributions. We argue in this paper that the Pareto-Lévy distribution is an interesting candidate for representing income distribution because its parameters are easy to interpret and it satisfies a specific invariance-under-aggregation property. We also demonstrate that the Gini coefficient can be expressed as a simple formula of the parameters of the Pareto-Lévy distribution. We subsequently use Terms of use: Documents in EconStor may

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“…Many authors have tackled the non-normality of high frequency financial variables from different perspectives ranging from non-parametric (Gallant and Tauchen, 1989;Robinson, 1995;Newley et al, 1998) to parametric estimation of the underlying density, assuming other specifications like the Student's t (Praetz, 1972;Blattberg and Gonedes, 1974;Rogalski and Vinso, 1978), jump processes (Ball and Torous, 1983;Jorion, 1988), mixtures of normal distributions (Hamilton, 1991;Peiró, 1995), or many other densities (McDonald and Newley, 1988;Baille and Bollerslev, 1990;Mittnik and Rachev, 1993;McDonald and Xu, 1995). This literature also accounts for the conditional heteroskedasticity phenomenon inherent in this kind of data (Bollerslev, 1987;Baillie and Bollerslev, 1989;Hsieh, 1989;Nelson, 1991;Ding et al, 1993;León and Mora, 1999), the ARCH and GARCH processes by Engle (1982) and Bollerslev (1986) being the most widely used.…”

Section: Introductionmentioning

confidence: 99%

Measuring Value at Risk of Portfolios under the Edgeworth-Sargan Distribution

Perote

Brio

2002

SSRN Journal

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Abstract:This paper sheds light on the evaluation of portfolio risk by assuming a distribution capable of incorporating the behaviour of most financial variables, especially at the tails: the so called Edgeworth-Sargan distribution. This density is preferable over other distributions, such as the Student's t, when fitting high frequency financial variables, because of its flexibility for improving data fits by adding more parameters in a natural way.Furthermore, this distribution is easy to be generalised to a multivariate context and, therefore, correlation coefficients among variables can be estimated efficiently. This article thus provides new insights into VaR methodology by estimating the joint density of portfolio variables, and by calculating the right critical values of the underlying portfolio density as well. The empirical examples include the estimation and evaluation of different volatility and weight scenarios for portfolios composed of stock indices and interest rates for major financial markets.

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A generalization of the beta distribution with applications

Cited by 406 publications

References 12 publications

An analysis of skewness and skewness persistence in three emerging markets

An analysis of skewness and skewness persistence in three emerging markets

Is the Pareto–Lévy law a good representation of income distributions?

Measuring Value at Risk of Portfolios under the Edgeworth-Sargan Distribution

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