Weighted quantile-based estimation for a class of transformation distributions

Rayner, G.D.; MacGillivray, Helen

doi:10.1016/s0167-9473(01)00090-1

Cited by 24 publications

(26 citation statements)

References 30 publications

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“…This has been carried out under both the frequentist (Rayner and MacGillivray 2002a;Su 2007) and Bayesian (Haynes and Mengersen 2005) paradigms. Alternatives include the starship method (King and MacGillivray 1999), while quantile-matching has been proposed for the g-and-k distribution (Rayner and MacGillivray 2002b). The use of approximate Bayesian computation for the parameter estimation problem will now be described, and a comparison with these methods made.…”

Section: Existing Methodsmentioning

confidence: 99%

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Bayesian estimation of quantile distributions

2008

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Use of Bayesian modelling and analysis has become commonplace in many disciplines (finance, genetics and image analysis, for example). Many complex data sets are collected which do not readily admit standard distributions, and often comprise skew and kurtotic data. Such data is well-modelled by the very flexibly-shaped distributions of the quantile distribution family, whose members are defined by the inverse of their cumulative distribution functions and rarely have analytical likelihood functions defined. Without explicit likelihood functions, Bayesian methodologies such as Gibbs sampling cannot be applied to parameter estimation for this valuable class of distributions without resorting to numerical inversion. Approximate Bayesian computation provides an alternative approach requiring only a sampling scheme for the distribution of interest, enabling easier use of quantile distributions under the Bayesian framework. Parameter estimates for simulated and experimental data are presented.

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Section: Existing Methodsmentioning

confidence: 99%

“…The parameter c measures the overall asymmetry, and, following standard practice, is fixed at 0.8 (Haynes 1998;Rayner and MacGillivray 2002b). Using this function, samples drawn from the standard normal distribution are transformed into samples from the g-and-k distribution with parameters A, B, g and k.…”

Section: The G-and-k Distributionmentioning

confidence: 99%

Bayesian estimation of quantile distributions

2008

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“…5, the histogram and the density plots show possible skewness and some outliers in both datasets. Following Rayner and MacGillivray (2002b), we use Tukey's g-and-h distribution to fit both datasets.…”

Section: Air Pollution Datamentioning

confidence: 99%

Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution

Genton

2015

Computational Statistics & Data Analysis

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“…Traditionally, quantile-based methods are applied to obtain estimates of the unknown parameters (see, e.g., Tukey, 1977or Rayner & MacGillivray, 2002a. Due to the increasing computing power, maximum likelihood estimation (MLE) which had been thought intractable can now be tackled numerically.…”

Section: Estimation Of Hjk-distributionsmentioning

confidence: 99%

“…Alternative transformations with existing moments but still heavy tails followed up by MacGillivray & Cannon's (1997) Ktransformation (see also Rayner & MacGillivray, 2002a, 2002b)…”

Section: Introductionmentioning

confidence: 99%

Generalized Tukey-type distributions with application to financial and teletraffic data

Fischer

2008

Stat Papers

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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 Constructing skew and heavy-tailed distributions by transforming a standard normal variable goes back to Tukey (1977) and was extended and formalized by Hoaglin (1983) and Martinez & Iglewicz (1984). Applications of Tukey's GH distribution family -which are composed by a skewness transformation G and a kurtosis transformation H -can be found, for instance, in financial, environmental or medical statistics. Recently, alternative transformations emerged in the literature. Rayner & MacGillivray (2002b) discuss the GK distributions, where Tukey's H-transformation is replaced by another kurtosis transformation K. Similarly, Fischer & Klein (2004) advocate the J-transformation which also produces heavy tails but -in contrast to Tukey's H-transformation -still guarantees the existence of all moments. Within this work we present a very general kurtosis transformation which nests H-, K-and J-transformation and, hence, permits to discriminate between them. Applications to financial and teletraffic data are given. Terms of use: Documents in EconStor may

show abstract

Weighted quantile-based estimation for a class of transformation distributions

Cited by 24 publications

References 30 publications

Bayesian estimation of quantile distributions

Bayesian estimation of quantile distributions

Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution

Generalized Tukey-type distributions with application to financial and teletraffic data

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