BACKGROUND AND PURPOSE Diffusional kurtosis imaging is an MR imaging technique that provides microstructural information in biologic systems. Its application in clinical studies, however, is hampered by long acquisition and postprocessing times. We evaluated a new and fast (2 minutes 46 seconds) diffusional kurtosis imaging method with regard to glioma grading, compared it with conventional dif...

We study the fourth-order moment of the cosmic shear field using the dark matter halo approach to describe the nonlinear gravitational evolution of structure in the universe. Since the third-order moment of the shear field vanishes because of symmetry, non-Gaussian signatures in its one-point statistics emerge at the fourth-order level. We argue that the shear kurtosis parameter Sγ,4 ≡ 〈γ i 〉c/...

We propose a nonlinear self-organising network which solely employs computationally simple hebbian and antihebbian learning in approximating a linear independent component analysis (ICA). Current neural architectures and algorithms which perform parallel ICA are either restricted to positively kurtotic data distributions [1] or data which exhibits one sign of kurtosis [2, 3, 12]. We show that t...

The amplitude of the El Niño-Southern Oscillation (ENSO) would be normally distributed if the coupled Pacific ocean-atmosphere were a linear system forced by Gaussian weather noise. Moment estimates of skewness and kurtosis demonstrate that this is not the case for monthly mean anomalies in Pacific sea surface temperatures during 1950-97. The noted predominance of El Niño events compared to La ...

As a practical measure of non-Gaussianity, kurtosis generally represents the preferred technique for signal extraction. Here a learning rule is presented associated with kurtosis. It can recover one source signal owning the maximum absolute value of kurtosis among all original sources. Computer simulations on biomedical signals demonstrate its efficiency. Introduction Blind source separation (B...

Background The spinal cord is a focus of many radiological diagnostics of such debilitating pathologies as multiple sclerosis, amytrophic lateral sclerosis, spondylosis, and post-traumatic injury. Since these disease states differentiate at the cellular level, diffusion-weighted imaging plays an important role due to its sensitivity to tissue microstructure and white matter connectivity. Most s...

The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In add...

This paper explores the ability of some popular income distributions to model observed skewness and kurtosis. We present the generalized beta type 1 (GB1) and type 2 (GB2) distributions’ skewnesskurtosis spaces and clarify and expand on previously known results on other distributions’ skewnesskurtosis spaces. Data from the Luxembourg Income Study are used to estimate sample moments and explore ...

The literature on portfolio analysis assumes that the securities returns are random variables with fixed expected returns and variances values (see Bachelier [1], Briec et al. [4] and Markowitz [10]). However, since investors receive efficient or inefficient information from the real world, ambiguous factors usually exist in it. Consequently, we need to consider not only random conditions but a...

The choice of demodulation band for envelope analysis of faulty bearings is often made by spectrum comparison with a healthy bearing, to choose resonance frequencies where the largest change occurred as a result of the fault. It has recently been established that the so-called “spectral kurtosis” gives a very similar indication of the band to be demodulated without requiring historical data. Th...