An appealing way of working with probability distributions, especially in nonparametric inference, is through “descriptive measures” that characterize features of particular interest. One attractive approach is to base the measures on quantiles. Here we consider the multivariate context and utilize the “spatial quantiles”, a recent vector extension of univariate quantiles that is becoming incre...

The standard root−b1 test is widely used for testing skewness. However, several studies have demonstrated that this test is not reliable for discriminating between symmetric and asymmetric distributions in the presence of excess kurtosis. The main reason for the failure of the standard root−b1 test is that its variance formula is derived under the assumption of no excess kurtosis. In this paper...

The probability density functions (PDFs) of sea level and geostrophic relative vorticity are examined using satellite altimeter data. It is shown that departures from a Gaussian distribution can generally be represented by two functions, and that the spatial distribution of these two functions is closely linked to the skewness and kurtosis of the PDF. The patterns indicate that strong jets tend...

BACKGROUND AND PURPOSE Despite being the gold standard technique for stroke assessment, conventional diffusion MRI provides only partial information about tissue microstructure. Diffusional kurtosis imaging is an advanced diffusion MRI method that yields, in addition to conventional diffusion information, the diffusional kurtosis, which may help improve characterization of tissue microstructure...

OBJECTIVES The aims of this study were to implement and systematically evaluate the performance of a new parameter-free segmented algorithm for analysis of diffusion imaging data using a combined intravoxel incoherent motion and diffusion kurtosis imaging (IVIM-DKI) model of spin diffusion in comparison with the simpler intravoxel incoherent motion (IVIM) model. MATERIALS AND METHODS A multis...

In this paper, we propose and study exp-kumaraswamy distribution. Some of its properties  are derived, including the density function, hazard rate function, quantile function, moments,  skewness  and kurtosis.   Adata set isused to illustrate an application of the proposed distribution. Also, we obtain a new distribution by transformation onexp-kumaraswamy distribution.   New distribution is an...

We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded variance or a bounded kurtosis. It turns out that these minimax deviations are of the same order as the deviations of the empirical mean estimator of a Gaussi...

PURPOSE To investigate associations between the clinicopathologic features and MRI features of triple-negative breast cancer (TNBC) and ER-positive breast cancer (BC) via apparent diffusion coefficient (ADC) histogram analysis. MATERIALS AND METHODS In this study, 221 breast cancer patients with pre-operative MRI performed from August 2009 to March 2015 were included in a retrospective analys...

Spectral Kurtosis (SK; defined by Nita et al. 2007) is a statistical approach for detecting and removing radio frequency interference (RFI) in radio astronomy data. In this paper, the statistical properties of the SK estimator are investigated and all moments of its probability density function are analytically determined. These moments provide a means to determine the tail probabilities of the...

PURPOSE To provide estimates of the diffusional kurtosis in the healthy brain in anatomically defined areas and list these along previously reported values in pathologies. MATERIALS AND METHODS Thirty-six volunteers (mean age = 33.1 years; range, 19-64 years) underwent diffusional kurtosis imaging. Mean kurtosis (MK), radial kurtosis (RK), mean diffusivity (MD), radial diffusivity (RD), and f...