High Kurtosis Values Research Articles

Maximum Likelihood Estimator for the Uneven Power Distribution: Application to DJI Returns

This paper deals with estimating peaked densities over the interval [0,1] using the Uneven Two-Sided Power Distribution (UTP). This distribution is the most complex of all the bounded power distributions introduced by Kotz and van Dorp (2004). The UTP maximum likelihood estimator, a result not derived by Kotz and van Dorp, is presented. The UTP is used to estimate the daily return densities of the DJI and stocks comprising this index. As the returns are found to have high kurtosis values, the UTP provides much more accurate estimations than a smooth distribution. The paper presents the program written in Mathematica which calculates maximum likelihood estimators for all members of the bounded power distribution family. The paper demonstrates that the UTP distribution may be extremely useful in estimating peaked densities over the interval [0,1] and in studying financial data.

Punctuated Equilibrium in Comparative Perspective

We explore the impact of institutional design on the distribution of changes in outputs of governmental processes in the United States, Belgium, and Denmark. Using comprehensive indicators of governmental actions over several decades, we show that in each country the level of institutional friction increases as we look at processes further along the policy cycle. Assessing multiple policymaking institutions in each country allows us to control for the nature of the policy inputs, as all the institutions we consider cover the full range of social and political issues in the country. We find that all distributions exhibit high kurtosis values, significantly higher than the Normal distribution which would be expected if changes in government attention and activities were proportionate to changes in social inputs. Further, in each country, those institutions that impose higher decision‐making costs show progressively higher kurtosis values. The results suggest general patterns that we hypothesize to be related to boundedly rational behavior in a complex social environment.

QSI and DTI of excised brains of the myelin-deficient rat

High b-value q-space diffusion imaging (QSI) and conventional DTI methodologies were used to study the MRI diffusion characteristics of excised brains of 21-day-old myelin-deficient ( md) rats and their age-matched controls. Three different indices were calculated from the QSI data, i.e., Displacement, Probability and Kurtosis, for the purpose of evaluating the effect of the myelin sheaths on the MR diffusion characteristics in white matter (WM) ROIs of the md versus control brains. The examined WM ROIs were the corpus callosum, the external capsule, and the internal capsule. In all examined WM ROIs, significant differences were observed between the md and control brains for all QSI indices. These differences reveal that myelin sheaths surrounding the axons in WM ROIs mostly affect the component exhibiting restricted diffusion, which is manifested by low mean displacement values and high probability and kurtosis values. Such differences were found to be more pronounced in long diffusion times, i.e., Δ = 200 ms. Conventional DTI performed with relatively low b-values ( b < 1500 s/mm 2) was also used to study md versus control brains. Interestingly, the fractional anisotropy (FA) index, which was calculated from DTI data, did not reveal any significant difference between the groups in the examined WM ROIs. However, some distinctions were revealed by the three eigenvalues ( λ 1, λ 2, and λ 3) obtained from the tensor analysis. These findings were supported by Voxel-based analysis using SPM. Finally, MRI-guided histology showed very good agreement between myelin-stained regions and regions with highly restricted diffusion detected by QSI.

Modelling spikes in electricity markets using excitable dynamics

We present a general methodology to model spikes in deregulated electricity markets using excitable dynamics in a multi-regime switching approach. In particular, we propose a two-regime switching model and a three-regime switching model in which the spikes phenomenon is described by a FitzHugh–Nagumo excitable dynamics. Both models seems to be interesting candidates for describing the main characteristics of electricity price dynamics as the occurrence of stable periods in which prices fluctuate around some long-run mean, and turbulent periods in which prices experience jumps and spikes of very large magnitude. In agreement with market data, both models can produce probability distributions of price returns with positive skewness and very high values of kurtosis.

1001 大気乱流拡散に関する風洞実験 : 可視化画像を利用した蛇行プルームの瞬間特性評価(2)(OS10-1 大気海洋の流体現象と環境流体,OS10 大気海洋の流体現象と環境流体,オーガナイズドセッション)

The characteristics of turbulent particle diffusion were investigated in a strong turbulence generated by an active turbulence generator installed to in a small wind tunnel. Instantaneous visualization image analysis was conducted on the plume's meandering motion using a digital camera for grid turbulence(R_λ=52) and excited turbulence(R_λ=526). To clarify the characteristics of the meandering plume, relative diffusion, meandering diffusion and total diffusion, as described in the Taylor's diffusion theory, were obtained by extracting the brightness values from a large number of instantaneous plume image pictures. In the excited turbulence accompanied by a wide inertial subrange, the time dependence on relative diffusion spread σ_r(T) showed almost the same tendency to the Batchelor's suggestions, i.e. 'σ_r∝T in thenear-field', '∝T^<3/2> in the intermediate-range' and '∝T^<1/2> in the far-field'. Meandering parameter σ_m was enhanced near the point source and then gradually increased as ∝ T^<1/2> downstream. Transverse relative diffusion was observed to have non-Gaussian profiles with high kurtosis value of 3.1〜9.6. The 'intermediate-field' was not clearly observed for the grid turbulence where only comparatively small scale vortexes acted, where σm increased only slightly near the source and become to be almost constant in the downstream region. Estimated based on the Gifford's model, the contribution rate of the relative diffusion and the meandering diffusion (σ_r/σ_m 19 to the total diffusion strongly depends on the turbulence Reynolds number of these turbulence fields.

Smoothing of the bivariate LOD score for non-normal quantitative traits.

Variance component analysis provides an efficient method for performing linkage analysis for quantitative traits. However, type I error of variance components-based likelihood ratio testing may be affected when phenotypic data are non-normally distributed (especially with high values of kurtosis). This results in inflated LOD scores when the normality assumption does not hold. Even though different solutions have been proposed to deal with this problem with univariate phenotypes, little work has been done in the multivariate case. We present an empirical approach to adjust the inflated LOD scores obtained from a bivariate phenotype that violates the assumption of normality.Using the Collaborative Study on the Genetics of Alcoholism data available for the Genetic Analysis Workshop 14, we show how bivariate linkage analysis with leptokurtotic traits gives an inflated type I error. We perform a novel correction that achieves acceptable levels of type I error.

Modeling the effect of skewness and kurtosis on the static friction coefficient of rough surfaces

Engineering surfaces possess roughnesses that exhibit asymmetrical height distributions. However, the Gaussian distribution is most often used to characterize the topography of surfaces, and is also used in models to predict contact and friction parameters. In this paper, the effects of kurtosis and skewness on different levels of surface roughness are investigated independently. This is accomplished by adopting the Pearson system of frequency curves and used in conjunction with a static friction model for rough surfaces to calculate the friction force and friction coefficient. This study is the first attempt to independently model the effect of kurtosis and skewness on the static friction and friction coefficient. It is predicted that surfaces with high kurtosis and positive skewness exhibit lower static friction coefficient compared to the Gaussian case. More importantly, it is predicted that, for high kurtosis values, the static friction coefficient decreases with decreasing external force rather than increasing as seen with increasing skewness. This is a very promising result for applications involving smooth lightly loaded contacts such as magnetic storage devices and microelectromechanical systems. The practical significance of the present model is specifically demonstrated on static friction predictions in magnetic storage head–disk interfaces. Such predictions can be used to determine the optimal characteristics of such devices prior to fabrication to achieve lower friction in terms of surface roughness, mechanical properties, apparent contact area, and operational environment.

Effect of winsorization on power and type 1 error of variance components and related methods of QTL detection.

Variance components analysis provides an efficient method for performing linkage analysis for quantitative traits. However, power and type 1 error of variance components-based likelihood ratio testing may be affected when phenotypic data are nonnormally distributed (especially with high values of kurtosis) and there is moderate to high correlation among the siblings. Winsorization can reduce the effect of outliers on statistical analyses. Here, we considered the effect of winsorization on variance components-based tests. We considered the likelihood ratio test (LRT), the Wald test, and some robust variance components tests. We compared these tests with Haseman-Elston least squares-based tests. We found that power to detect linkage is significantly increased after winsorization of the nonnormal phenotypes. Winsorization does not greatly diminish the type 1 error for the variance components-based tests for markedly nonnormal data. A robust version of the LRT that adjusts for sample kurtosis showed the best power for nonnormal data. Finally, phenotype winsorization of nonnormal data reduces the bias in estimation of the major gene variance component.

A blind interpretation of drill‐bit signals

The role of kurtosis in evaluating the quality of vertical seismic profiling (VSP) drill‐bit data is investigated. The calculations show how kurtosis depends on the dominant frequency, bandwidth, and phase content of a seismic signal. This analysis is applied to synthetic and real common‐offset and common‐shot drill‐bit seismograms to evaluate the prominence and quality of the first arrival and other coherent events. High values of kurtosis correspond to an isolated first arrival or to a compressed coherent noise event, while low values are typical of low S/N (distributed) ratio traces. Kurtosis analysis applied to drill‐bit VSP data while drilling proved to be successful at identifying high‐quality traces with little interpretational input.

Surface characterisation of electro-active thin polymeric film bearings

We report the results of a recent study of tribological properties of electropolymerised thin film bearings. Poly(pyrrole) films of different thickness and incorporating different counter ions have been grown onto gold electrodes on glass lens substrates and tested under a pin-on-disk apparatus. The topography of the films has been studied in order to set up correlation between surface parameters and the tribological functions, which is in turn to identify crucial parameters in the film processes for an optimum surface performance. Based upon this study, roughness distribution parameter, skewness and kurtosis are playing an important role in controlling friction. Film surfaces with positive skewness and high kurtosis values are favourable for low friction bearings.

Shaker Simulation of Random Vibration with a High Kurtosis Value

This paper presents a vibration test technique for extending the tails of amplitude probability distribution beyond the Gaussian values as is characteristic for vibration of ground vehicles on a rough road or terrain. The method proposed uses the commonly accepted approach of applying pseudorandom excitation in the form of a Fourier expansion. The procedure described in this paper can be implemented by updating currently available digital vibration controllers. The solution for amplitude domain fitting is based on an analytical expression derived for the kurtosis parameter of the polyharmonic process in terms of amplitudes and phase angles for any number of harmonic components. The results of theoretical analysis are embodied in software subjected to verification in computer and experimental tests. Even with additional kurtosis control, the closeness of the generated and desired spectra is the same as for the Gaussian simulation of power spectral density. Hence, this new technique for amplitude domain matching is not accompanied by the deterioration of ordinary test capabilities in the frequency domain.

Non-Gaussian surface roughness distribution of magnetic media for minimum friction/stiction

Contact of two rough surfaces at an interface occurs at a small fraction of the nominal area. The real area of contact and interfacial adhesion primarily control the friction of an interface. With the presence of a thin film of liquid lubricant or adsorbed water layer at the interface, menisci form around the contacting and near-contacting asperities. The meniscus formation results in stiction problems in the head–medium interfaces. The objective of this research is to predict optimum surface roughness for minimum friction/stiction. For the first time, the effects of skewness and kurtosis of surfaces with non-Gaussian distribution on contact area and meniscus contribution have been studied. A numerical model that accounts for the effects of roughness distribution and liquid film was used for this study. Based on this study, a surface with non-Gaussian distribution with positive skewness between 0 and 0.2 and/or with high values of kurtosis (K≥5) should be used for low friction and stiction.

Minimum entropy deconvolution of underwater acoustic transients

The minimum entropy deconvolution (MED) method [R. Wiggins, Geoexploration 16, 21–35 (1978)], is used to produce source signature estimates from underwater acoustic transients, which has application in the passive sonar classification problem. The Green’s function, representing environmental distortion effects, is treated as a non‐Gaussian random process. The MED method implemented in this paper leads to a one‐parameter model that doesn’t require accurate knowledge of the source location and environmental parameters, or the computation of Green’s functions. Results from applying the MED method to single‐sensor, broadband ocean acoustic measurements are shown, where source signature estimate correlation coefficients range between 0.87 to 0.91. The method is also applied to realistic simulations, produced with a parabolic equation (PE) model, using a source pulse that was longer and more complex than the measured source. Source signature estimate correlation coefficients ranged between 0.95 and 0.99. The technique assumes that the input random process is non‐Gaussian, which is justified by high kurtosis values of the computed (PE) Green’s functions associated with this data set. [Work supported by Office of Naval Research, with technical management provided by the Naval Research Laboratory.]

Depth profiles of Sb atoms implanted into Ti

Abstract The parameters of the depth profiles of Sb atoms implanted into titanium were measured using standard RBS technique. The measured profile moments are compared with theoretical values calculated by means of TRIM program. The experimental projected ranges are lower by 15–25% than the theoretical ones but these differences may partly be explained by target sputtering. The measured range stragglings agree with those calculated within few percent. Extremely high values of profile skewness and kurtosis are found for shallow profiles.