Power kurtosis transformations: Definition, properties and ordering

Klein, Ingo; Fischer, Matthias

doi:10.1007/s10182-006-0241-1

Cited by 5 publications

(3 citation statements)

References 4 publications

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“…The branch length and radius data for the whorl-level analysis were log-transformed. The data for the branch-level analysis were subjected to an optimizing (iterated) Box-Cox transformation, followed by a monotonic, inverse-errorfunction correction to mitigate negative kurtosis caused by excessive tail compression by the Box-Cox transformation (Klein and Fischer, 2006). All transformed data beyond four standard deviations about the mean were excluded from the analyses (<0.1% of the total datasets).…”

Section: Discussionmentioning

confidence: 99%

Environmental Pollution

2006

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Canopy architecture and stem flow are affected by elevated CO 2 and tropospheric O 3 . a r t i c l e i n f o a b s t r a c tThe forest hydrologic budget may be impacted by increasing CO 2 and tropospheric O 3 . Efficient means to quantify such effects are beneficial. We hypothesized that changes in the balance of canopy interception, stem flow, and through-fall in the presence of elevated CO 2 and O 3 could be discerned using image analysis of leafless branches. We compared annual stem flow to the results of a computerized analysis of all branches from the 2002, 2004, and 2006 annual growth whorls of 97 ten-year-old trees from the Aspen Free-Air CO 2 and O 3 Enrichment (Aspen FACE) experiment in Rhinelander, WI. We found significant effects of elevated CO 2 and O 3 on some branch metrics, and that the branch metrics were useful for predicting stem flow from birch, but not aspen. The results of this study should contribute to development of techniques for efficient characterization of effects on the forest hydrologic budget of increasing CO 2 and tropospheric O 3 .

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Section: Discussionmentioning

confidence: 99%

Environmental Pollution

2006

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“…Moreover, Klein and Fischer (2006) showed that the parameter γ can also be interpreted as a skewness parameter in terms of the partial ordering proposed by van Zwet (1964). This reparameterisation can also be used in DTP distributions for inducing orthogonality between σ and γ through parameterisations that satisfy a(γ) + b(γ) = constant.…”

Section: Reparameterisationsmentioning

confidence: 94%

“…Some examples of skewing mechanisms can be found in Azzalini (1985) and Fernández and Steel (1998a). Examples of elongations can be found in Hoaglin et al (1985), Haynes et al (1997), Fischer and Klein (2004), and Klein and Fischer (2006). A third class of transformations consists of those that contain two parameters that are used for modelling skewness and kurtosis jointly.…”

Section: Introductionmentioning

confidence: 99%

Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions

Rubio¹,

Steel²

2015

Electron. J. Statist.

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We formalise and generalise the definition of the family of univariate double two-piece distributions, obtained by using a densitybased transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting distributions contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of distributions that capture different types of asymmetry are discussed. We propose interpretable scale and location-invariant benchmark priors and derive conditions for the propriety of the corresponding posterior distribution. The prior structures used allow for meaningful comparisons through Bayes factors within flexible families of distributions. These distributions are applied to data from finance, internet traffic and medicine, comparing them with appropriate competitors.

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