. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii CHAPTER 1. GENERAL INTRODUCTION . . . . . . . . . . . . . . . . . . . 1 1.1 One-way Random Effects ANOVA Model . . . . . . . . . . . . . . . . . . . . . 1 CHAPTER 2. REVIEW OF LITERATURE . . . . . . . . . . . . . . . . . . . . 5 2.1 The Statistical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Constructing skew and heavy-tailed distributions by transforming a standard normal variable goes back to Tukey (1977) and was extended and formalized by Hoaglin (1983) and Martinez & Iglewicz (1984). Applications of Tukey’s GH distribution family – which are composed by a skewness transformation G and a kurtosis transformation H – can be found, for instance, in financial, environmental or medic...

The probability density function (PDF) of the surface electromyogram (EMG) signals has been modelled with Gaussian and Laplacian distribution functions. However, a general consensus upon the PDF of the EMG signals is yet to be reached, because not only are there several biological factors that can influence this distribution function, but also different analysis techniques can lead to contradic...

The purpose of this study was to evaluate the effect of a forest environment on salivary cortisol concentration, particularly on the characteristics of its distribution. The participants were 348 young male subjects. The experimental sites were 34 forests and 34 urban areas across Japan. The subjects viewed the landscape (forest or urban environment) for a period of 15 min while sitting in a ch...

In this paper, a comparative study between proposed hyper kurtosis based modified duo-histogram equalization (HKMDHE) algorithm and contrast limited adaptive histogram enhancement (CLAHE) has been presented for the implementation of contrast enhancement and brightness preservation of low contrast human brain CT scan images. In HKMDHE algorithm, contrast enhancement is done on the hyper-kurtosis...

An expression for the second-order approximation to the kurtosis associated with the least squares estimate of an individual parameter in a nonlinear regression model is derived, and connections between this and various other measures of curvature are made. Furthermore a means of predicting the reliability of the commonly-used Wald confidence intervals for individual model parameters, based on ...

Exploratory data analysis statistics, such as those generated by the SAS® procedure PROC UNIVARIATE (1990), are useful tools to characterize the underlying distribution of data prior to more rigorous statistical analyses. Assessment of the distributional shape of data is usually accomplished by careful examination of the values of the third and fourth central moments, skewness and kurtosis. How...

We obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes. Analogous to a well known lower bound on the randomness parameter, the lower bounds on skewness and kurtosis are related to the number of intermediate states in the underlying chemical reaction network. Our results demonstrate that evaluating these hig...

1 We derive formulae for the higher order tail moments of the lower truncated multivariate standard normal (MVSN), Student’s t, lognormal and a finite-mixture of multivariate normal distributions (FMVN). For the MVSN we propose a recursive formula for moments of arbitrary order as a generalization of previous research. For the Student’s t-distribution, the recursive formula is an extension of t...

Diffusional kurtosis imaging (DKI), which measures the non-Gaussianity of water diffusion, has been demonstrated to be a sensitive biomarker in many neuropathologies. The goal of this study was to longitudinally examine the spatiotemporal dynamics of DKI in cerebral ischemia in an animal model of permanent and transient (45 min) middle cerebral artery occlusion (MCAO) during the hyperacute, acu...