Diffusion of water molecules in biological tissues is conventionally quantified via diffusion tensor imaging (DTI) [1]. DTI enables a Gaussian approximation to the probability distribution governing the random displacement of water molecules. In some circumstances of great interest, however, the displacement probability distribution can deviate considerably from a Gaussian form. Diffusional kur...

MR diffusion kurtosis imaging (DKI) was proposed recently to study the deviation of water diffusion from Gaussian distribution. Mean kurtosis, the directionally averaged kurtosis, has been shown to be useful in assessing pathophysiological changes, thus yielding another dimension of information to characterize water diffusion in biological tissues. In this study, orthogonal transformation of th...

"Kurtosis" has long been considered an appropriate measure to quantify the extent of fat-tailedness of the degree distribution of a complex real-world network. However, the Kurtosis values for more than one realworld network have not been studied in conjunction with other statistical measures that also capture the extent of variation in node degree. Also, the Kurtosis values of the distribution...

The kurtosis coefficient is often regarded as a measure of the tail heaviness of a distribution relative to that of the normal distribution. However, it also measures the peakedness of a distribution, hence there is no agreement on what kurtosis really estimates. Another disadvantage of the kurtosis is that its interpretation and consequently its use is restricted to symmetric distributions. Mo...

This paper presents a parsimonious approach to estimating conditional skewness and kurtosis, as well as conditional variance, in financial log-returns time series. Using a GARCH formulation of the skew t-distribution (Jones and Faddy, 2003), autoregressive relationships are developed for the conditional skewness and conditional kurtosis. A numerical example indicates that allowing for estimates...

Introduction In contrast to free diffusion, the restrictions present in biological tissue cause the diffusion propagator to deviate from a Gaussian function. Diffusion kurtosis imaging (DKI) [1,2] extends Diffusion Tensor Imaging (DTI) in order to quantify these deviations from Gaussian behaviour yielding additional information about the tissue microstructure. To calculate the kurtosis, diffusi...

Engle and Manganelli (2004) propose CAViaR, a class of models suitable for estimating conditional quantiles in dynamic settings. Engle and Manganelli apply their approach to the estimation of Value at Risk, but this is only one of many possible applications. Here we extend CAViaR models to permit joint modeling of multiple quantiles, Multi-Quantile (MQ) CAViaR. We apply our new methods to estim...

This paper presents a new algorithm making use of kurtosis, which is a statistical parameter, to distinguish the seismic signal generated by a person's footsteps from other signals. It is adaptive to any environment and needs no machine study or training. As persons or other targets moving on the ground generate continuous signals in the form of seismic waves, we can separate different targets ...