Skew-symmetric distributions and Fisher information -- a tale of two densities

Skew-symmetric densities recently received much attention in the literature, giving rise to increasingly general families of univariate and multivariate skewed densities. Most of those families, however, suffer from the inferential drawback of a potentially singular Fisher information in the vicinity of symmetry. All existing results indicate that Gaussian densities (possibly after restriction to some linear subspace) play a special and somewhat intriguing role in that context. We dispel that widespread opinion by providing a full characterization, in a general multivariate context, of the information singularity phenomenon, highlighting its relation to a possible link between symmetric kernels and skewing functions -- a link that can be interpreted as the mismatch of two densities.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ346 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A general method for the statistical evaluation of typological distributions

The distribution of linguistic structures in the world is the joint product of universal principles, inheritance from ancestor languages, language contact, social structures, and random fluctuation. This paper proposes a method for evaluating the relative significance of each factor — and in particular, of universal principles — via regression modeling: statistical evidence for universal principles is found if the odds for families to have skewed responses (e.g. all or most members have postnominal relative clauses) as opposed to having an opposite response skewing or no skewing at all, is significantly higher for some condition (e.g. VO order) than for another condition, independently of other factors

Flexible modelling in statistics: past, present and future

In times where more and more data become available and where the data exhibit rather complex structures (significant departure from symmetry, heavy or light tails), flexible modelling has become an essential task for statisticians as well as researchers and practitioners from domains such as economics, finance or environmental sciences. This is reflected by the wealth of existing proposals for flexible distributions; well-known examples are Azzalini's skew-normal, Tukey's $g$-and-$h$, mixture and two-piece distributions, to cite but these. My aim in the present paper is to provide an introduction to this research field, intended to be useful both for novices and professionals of the domain. After a description of the research stream itself, I will narrate the gripping history of flexible modelling, starring emblematic heroes from the past such as Edgeworth and Pearson, then depict three of the most used flexible families of distributions, and finally provide an outlook on future flexible modelling research by posing challenging open questions.Comment: 27 pages, 4 figure

Comparison of Induction and PM Synchronous motor drives for EV application including design examples

Three different motor drives for electric traction are compared, in terms of output power and efficiency at the same stack dimensions and inverter size. Induction motor (IM), surface-mounted permanent-magnet (PM) (SPM), and interior PM (IPM) synchronous motor drives are investigated, with reference to a common vehicle specification. The IM is penalized by the cage loss, but it is less expensive and inherently safe in case of inverter unwilled turnoff due to natural de-excitation. The SPM motor has a simple construction and shorter end connections, but it is penalized by eddy-current loss at high speed, has a very limited transient overload power, and has a high uncontrolled generator voltage. The IPM motor shows the better performance compromise, but it might be more complicated to be manufactured. Analytical relationships are first introduced and then validated on three example designs and finite element calculated, accounting for core saturation, harmonic losses, the effects of skewing, and operating temperature. The merits and limitations of the three solutions are quantified comprehensively and summarized by the calculation of the energy consumption over the standard New European Driving Cycl

A Constructive Representation of Univariate Skewed Distributions

We introduce a general perspective on the introduction of skewness into symmetric distributions. Making use of inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the effects of the skewing mechanism on \emph{e.g.} modality, tail behaviour and the amount of skewness generated. In light of the constructive representation, we review a number of characteristics of three classes of skew distributions previously defined in the literature. The representation is also used to introduce two novel classes of skewed distributions. Finally, we incorporate the different classes of distributions into a Bayesian linear regression framework and analyse their differences and similarities.Arnold and Groeneveld skewness measure, Bayesian regression model, inverse probability integral transformation, modality, skewing mechanism, tail behaviour

Skewed Parton Distributions and F_2^D at beta -> 1

We show that the diffractive structure function is perturbatively calculable in the domain where the diffractive mass is small but still outside the resonance region. In this domain, which can be characterized by Lambda^2/Q^2 << 1-beta << (Lambda^2/Q^2)^1/2, the structure function represents a new observable, which is highly sensitive to the small-x skewed gluon distribution. Our leading order calculation and the estimate of next-to-leading order corrections are consistent with available data and demonstrate the potential of more precise data to put further constraints on skewing effects.Comment: 11 pages, LaTeX, including five PostScript figure