Excess Kurtosis Research Articles

Influence of thickness, homogeneity, and morphology of TiO2-m nanoparticle coatings on cancer cell adhesion

In the last decades great advances have been made in the photodynamic therapy (PDT) of different types of cancer using TiO 2 nanoparticles. However, while most of these have been applied on adherent cancer cells, few reports show the application of PDT to non-adherent cancers such as leukemia, due to inherent challenges related to the selective targeting and irradiation of non-adherent cancer cells. As a possible solution for this issue, coatings based on modified TiO 2 (TiO 2 -m) nanoparticles have been shown to exhibit remarkable selectivity for trapping non-adherent cancer cells without additional binding agents such as aptamers or antibodies. To elucidate the influence of deposition conditions and film morphology on cell adhesion, we have coated glass slides with TiO 2 -m nanoparticles by dip coating according to a 2 2 factorial experimental design. The physicochemical surface properties of the TiO 2 -m nanoparticle coatings were characterized for different deposition conditions and correlated with their performance in trapping leukemic cells. Surface statistical parameters such as root-mean-square (RMS) surface roughness , roughness factor, and height distribution were determined by atomic force microscopy , while coating thickness and homogeneity were assessed by UV transmittance and Raman spectroscopy , respectively. The biological tests showed that the adhesion of leukemic cells on the TiO 2 -m nanoparticle coating depends on multiple parameters with layer homogeneity and the higher-order surface morphological parameters skewness (Ssk) and excess kurtosis (Sks) playing particularly important roles. By maximizing layer homogeneity and minimizing both Ssk and Sks, we were able to obtain a more than threefold increase in the cell adhesion factor after 24 h incubation. • TiO 2 -m coatings selectively trap non-adherent cancer cells at short contact times. • Surface parameters of the coating influence leukemic cell adhesion. • Low kurtosis and skewness values promote leukemic cells adhesion. • Combining Ssk, Sks, Sq and homogeneity values increases the number of trapped cells.

Detecting periodically collapsing bubbles in the S&P 500

Two robust tests on S&P 500 data show evidence of bubbles. A test of stationarity controlling for skewness and excess kurtosis is designed to detect periodically collapsing rational bubbles. Test for cointegration and direct tests on the price-dividend and price-earnings ratios cannot reject non-stationarity for all the samples considered. A test for explosive behavior on rolling window of the data also provide evidence of multiple bubbles and allow for dating of bubbles using the same set of variables. The two bubble episodes detected in all relevant cases are associated with the Spanish Flu in 1917 and the housing crisis in 2008.

On the Risk of Novel Specialized REITs

Under the multivariate GARCH framework, we examined the risk characteristics of six groups of novel specialized REITs in the United States, which had experienced significant changes from 2004 to 2019. The six groups are healthcare, hotel, self-storage, mortgaged-backed security (MBS), high-tech, and timber REITs. Results show that the six specialized REIT groups displayed different patterns of volatility surrounding the 2007–2009 financial crisis. The volatilities and dynamic conditional correlations (DCC) reached their peaks during the financial crisis and recovered two years afterwards. Mostly positive DCCs imply that the diversification effect was weak among the specialized REIT groups. Specialized REITs exhibited lower risks than the overall market. Among the three subsample (pre-crisis, crisis, and post-crisis) periods and across all specialized REIT groups, conditional variance was the smallest and excess kurtosis was the largest over the pre-crisis period; constant variance was the largest during the crisis; and skewness was the largest and correlations were the most volatile after the crisis. For individual REIT groups, healthcare and hotel REITs had the smallest and largest excess kurtosis; MBS and hotel REITs had the smallest and largest systematic and total risks; and self-storage and MBS REITs had the weakest and strongest leverage effect, respectively. In addition, high-tech REITs had the largest mean returns as well as increasing time-varying correlations with other groups before the crisis, and healthcare and high-tech REITs had more skewed returns than MBS and timber REITs.

Properties of the C ii 1334 Å Line in Coronal Hole and Quiet Sun as Observed by IRIS

Abstract Coronal holes (CHs) have subdued intensity and net blueshifts when compared to the quiet Sun (QS) at coronal temperatures. At transition region temperatures, such differences are obtained for regions with identical absolute photospheric magnetic flux density (∣B∣). In this work, we use spectroscopic measurements of the C ii 1334 Å line from the Interface Region Imaging Spectrograph, formed at chromospheric temperatures, to investigate the intensity, Doppler shift, line width, skew, and excess kurtosis variations with ∣B∣. We find the intensity, Doppler shift, and linewidths to increase with ∣B∣ for CHs and QS. The CHs show deficit in intensity and excess total widths over QS for regions with identical ∣B∣. For pixels with only upflows, CHs show excess upflows over QS, while for pixels with only downflows, CHs show excess downflows over QS that cease to exist at ∣B∣ ≤ 40. Finally, the spectral profiles are found to be more skewed and flatter than a Gaussian, with no difference between CHs and QS. These results are important in understanding the heating of the atmosphere in CH and QS, including solar wind formation, and provide further constraints on the modeling of the solar atmosphere.

Аналіз кумулянтних коефіцієнтів двокомпонентних сумішей зсунутих негаусових розподілів

The dependence of the cumulant coefficients of two-component mixtures of shifted non- Gaussian distributions on the weight coefficient is analyzed and conditions are determined under which the cumulant coefficients of any orders are equal to zero. The dependence of the cumulant coefficients of two-component mixtures on the shear parameter is investigated and the parameter values are determined at which the cumulant coefficients of any orders have extrema and zeros. The dependence of the skewness and excess kurtosis of a two-component mixture of shifted Gumbel distributions of type 1 on the weight coefficient and the shear parameter is investigated and their values are obtained at which the skewness and excess kurtosis of the mixture are equal to zero. The features of computer modeling of random variables, the probability density of which is a two-component mixture of shifted distributions, are considered.

A Moments View of Climatology and Variability of the Asian Summer Monsoon Anticyclone

AbstractA comprehensive investigation of the climatology of and interannual variability and trends in the Asian summer monsoon anticyclone (ASMA) is presented, based on a novel area and moments analysis. Moments include centroid location, aspect ratio, angle, and “excess kurtosis” (measuring how far the shape is from elliptical) for an equivalent ellipse with the same area as the ASMA. Key results are robust among the three modern reanalyses studied. The climatological ASMA is nearly elliptical, with its major axis aligned along its centroid latitude and a typical aspect ratio of ~5–8. The ASMA centroid shifts northward with height, northward and westward during development, and in the opposite direction as it weakens. New evidence finding no obvious climatological bimodality in the ASMA reinforces similar suggestions from previous studies using modern reanalyses. Most trends in ASMA moments are not statistically significant. ASMA area and duration, however, increased significantly during 1979–2018; the 1958–2018 record analyzed for one reanalysis suggests that these trends may have accelerated in recent decades. ASMA centroid latitude is significantly positively (negatively) correlated with subtropical jet-core latitude (altitude), and significantly negatively correlated with concurrent ENSO; these results are consistent with and extend previous work relating monsoon intensity, ENSO, and jet shifts. ASMA area is significantly positively correlated with the multivariate ENSO index 2 months previously. These results improve our understanding of the ASMA using consistently defined diagnostics of its size, geometry, interannual variability, and trends that have not previously been analyzed.

Daily stock prices prediction using variance gamma model

The Black-Scholes-Merton model is often used for modeling company assets, which requires normally distributed data. The company's asset price fluctuates greatly, causing the form of data distribution to allow for heavy tails, asymmetry and excess kurtosis. Therefore we need a model that can capture this phenomenon. The model is the Variance Gamma model, abbreviated as VG. The assumption of normality in the Black-Sholes-Merton theory is unable to capture the heavy tail and the asymmetry that exists in the log returns asset. This form of density usually that is too high compared to normal density is known as excess kurtosis. The additional parameters in the VG process can overcome heavy tail, asymmetry and excess kurtosis. These parameters can control the kurtosis, asymmetry, and adjust the slope of the log asset density. The VG process can be obtained from two approaches. First, the VG process as a change in Brownian motion to Gamma time, abbreviated as VG1. Second, the VG process is obtained by the difference of the two Gamma processes, abbreviated as VG2. In this study we applied the VG model to predict the daily stock price of PT Bank Negara Indonesia (Persero) Tbk. The results obtained show that the VG model provides accurate daily stock price prediction results.

On two approaches to the third-order solution of surface gravity waves

A third-order approximate solution for surface gravity waves in the finite water depth is studied in the context of potential flow theory. This solution corresponds to the steady-state part of a multidirectional irregular wave field and provides explicit expressions for the surface elevation, free-surface velocity potential, and velocity potential. The amplitude dispersion relation is also provided. Two approaches are used to derive the third-order analytical solution, resulting in two types of approximate solutions: the perturbation solution and the Hamiltonian solution. The perturbation solution is obtained by a classical perturbation technique in which the time variable is expanded in multiscale to eliminate secular terms. The Hamiltonian solution is derived from the canonical transformation in the Hamiltonian theory of water waves. By comparing the two types of solutions, it is found that they are completely equivalent for the first- and second-order solutions and the nonlinear dispersion, but for the third-order part only the sum–sum terms are the same. Due to the canonical transformation that could completely separate the dynamic and bound harmonics, the Hamiltonian solutions break through the difficulty that the perturbation theory breaks down due to singularities in the transfer functions when the quartet resonance criterion is satisfied. Furthermore, it is also found that some time-averaged quantities based on the Hamiltonian solution, such as mean potential energy and mean kinetic energy, are equal to those in the initial state in which the sea surface is assumed to be a Gaussian random process. This is because there are associated conserved quantities in the Hamiltonian form. All of these show that the Hamiltonian solution is more reasonable and accurate to describe the third-order steady-state wave field. Finally, based on the Hamiltonian solution, some statistics are given such as the volume flux, skewness, excess kurtosis, and non-uniqueness of the induced mean flow and mean surface.

OPTION IMPLIED VIX, SKEW AND KURTOSIS TERM STRUCTURES

Comparisons are made of the Chicago Board of Options Exchange (CBOE) skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies can be due to strike discretization in evaluating prices of powered returns. The remedy suggested employs a finer and wider set of strikes obtaining additional option prices by interpolation and extrapolation of implied volatilities. Procedures of replicating powered return claims are applied to the fourth power and the derivation of kurtosis term structures. Regressions of log skewness and log excess kurtosis on log maturity confirm the positivity of decay in these higher moments. The decay rates are below those required by processes of independent and identically distributed increments.

The Influence of Confidence and Social Networks on an Agent-Based Model of Stock Exchange

This paper aims to investigate the influence of investors’ confidence in their portfolio holding relative to their social group and of various social network topologies on the dynamics of an artificial stock exchange. An investor’s confidence depends on the growth rate of his or her wealth relative to his or her social group’s average wealth. If the investor’s confidence is low, the agent will change his or her asset allocation; otherwise, he or she will maintain it. We consider three types of social networks: Barabási, small-world, and random. The actual stock markets’ properties are recovered by this model: high excess kurtosis, skewness, volatility clustering, random walk prices, and stationary return rates. The networks’ topologies are found to impact both the structuration of investors in the space of strategies and their performance. Among other characteristics, we find that (i) the small-world networks show the highest degree of homophily; (ii) as investors can switch to more profitable strategies, the best approach to make profitable investments is the chartist one in Barabási and small-world topologies; and (iii) an unequal distribution and more significant relative wealth gains occur in the Barabási network.

Variance gamma for stock model performance with excess kurtosis

The Geometric Brownian Motion (GBM) model is used widely for model the dynamic of asset price movement. One of the company’s assets is a stock. The distribution of stock data that is normally distributed can be modeled using the Geometric Brownian Motion model. However, the distribution of stock data showed excess kurtosis and tail when using the Brown Geometry Motion model was less precise. One model for data showing excess kurtosis and tail was Variance Gamma (VG). In this research, the sample used was the stock data of PT Bank Danamon Indonesia Tbk for the period April 25 th , 2018 to April 24 th , 2020. The data sample was divided into two parts, namely training data and testing data. Based on the result of the stock description statistics, the value of skewness = -2.105417 and kurtosis = 22.16438 was obtained, while hypothesis testing concluded that the stock distribution did not spread normally. The resulting parameters for the VG model were σ = 0.08071, v = 8.00500 and θ = 0.01976. Based on the results of testing on the last 38 observations, the MAPE value was = 6.97560%. These results gave the conclusion that the VG model provided excellent forecasting results.

Two component modified Lilliefors test for normality

Research background: Commonly known and used parametric tests e.g. Student, Behrens? Fisher, Snedecor, Bartlett, Cochran, Hartley tests are applicable when there is an evidence that samples come from the Normal general population. What makes things worse is that testers are not fully aware in what degree of abnormality distorts results of parametric tests listed above and suchlike. So, it is no exaggeration to say that testing for normality (goodness-of-fit testing, GoFT) is a gate to proper parametric statistical reasoning. It seems that the gate opens too easily. In other words, most popular goodness-of-fit tests are weaker than statisticians want them to be.
 Purpose of the article: The main purpose of this paper is to put forward the GoFT that is, in particular circumstances, more powerful than GoFTs used until now. The other goals are to define a similarity measure between an alternative distribution and the normal one and to calculate the power of normality tests for a big set of alternatives. And, of course, to interest statisticians in using the GoFTs in their practice.
 Method: There are two ways to make GoFT more powerful: extensive and intensive one. The extensive method consists in drawing large samples. The intensive method consists in extracting more information from mall samples. In order to make the test method intensive, the test statistics, as distinct from all existing GoFTs, has two components. The first component (denoted by ?) is a classic Kolmogorov / Lilliefors test statistics i.e. the greatest absolute difference between theoretical and empirical cumulative distribution functions. The second component is the order statistics (r) at which the ?_max^((r) ) locate itself. Of course ?_max^((r) ) is the conditional random variable with (r) being the condition. Large scale Monte Carlo simulations provided data sufficient to in-depth study of properties of distributions of ?_max^((r) ) random variable.
 Findings & value-added: Simulation study shows that the Two Component Modified Lilliefors test for normality is the most powerful for some type of alternatives, especially for the symmetrical, unimodal and bimodal distributions with positive excess kurtosis, for symmetrical and unimodal distributions with negative excess kurtosis and small sample sizes. Due to the values of skewness and excess kurtosis, and the defined similarity measure between the ND and an alternative, alternative distributions are close to the normal distribution. Numerous examples of real data show the usefulness of the proposed GoFT.

Effect of non-ambient pressure conditions and Lewis number variation on direct numerical simulation of turbulent Bunsen flames at low turbulence intensity

The instantaneous flame front structure of high pressure turbulent premixed Bunsen flames has been analyzed for a wide range of characteristic Lewis numbers using a new Direct Numerical Simulation (DNS) database. High pressure turbulent premixed flames of lean-light fuels are likely to feature both thermo-diffusive and Darrieus–Landau instabilities. As the effects of these instabilities are eclipsed by intense turbulence, the present analysis focuses on flames located at the border of the wrinkled and corrugated flamelets regimes. The flame morphology has been characterized by the skewness and kurtosis of the probability density function (PDF) profiles of the mean and Gaussian curvatures. While skewness alone is not sufficient as a marker to distinguish between thermo-diffusive and Darrieus–Landau instabilities, it has been found that excess kurtosis of Gaussian curvature possibly can be used to distinguish between both instabilities. Further, the inner cut-off length and the fractal dimension have been computed for characterization of flame scales and for parameterization of wrinkling factor models. It has been observed that increasing pressure and decreasing Lewis number give rise to flame instabilities which results in an increased fractal dimension and a decreased inner cut-off scale. For high pressure flames with Lewis numbers around unity, the inner cut-off scale scales very well with the critical wavelength for flame instabilities determined from the theoretical analysis by Matalon and Matkowsky (1982). For small sub-unity Lewis numbers, the flames become unconditionally unstable and the critical wavelength loses its meaning, while the inner cut-off scales continues to decrease with Lewis number and the fractal dimension continues to increase up to a limit of about 7/3. The present findings are in excellent agreement with experimental observations from literature and theoretical analysis of flame instabilities.

Evolution of waves in a horizontal pipe propagating on a surface of a liquid film sheared by gas

Different wavy regimes in stratified air–water pipe flow are determined for a wide range of gas and liquid flow rates in a 10 m long horizontal pipe with a diameter of 24 mm. Three sub-regions of wavy stratified flow are identified: ripples, roll waves, and pre-annular wavy flow. Statistical parameters, such as local mean film thickness and its higher moments (root-mean-square, skewness, excess kurtosis) as well as wave characteristics (mean heights and wave height distributions, lengths, propagation velocities, etc.), are measured and analyzed. It is demonstrated that ripples are essentially linear waves and their propagation velocities are described reasonably well by linear wave theory. High amplitude roll and pre-annular waves are substantially nonlinear, and their propagation velocities differ significantly from that of ripples. Transition to roll waves causes a sharp increase in higher statistical moments. Evolution of wave and statistical parameters characterizing each sub-region of stratified gas–liquid pipe flow is studied. Simplified models describing roll waves are presented; the model predictions are verified by experiments.

Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions

The local number variance associated with a spherical sampling window of radius $R$ enables a classification of many-particle systems in $d$-dimensional Euclidean space according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To better characterize density fluctuations, we carry out an extensive study of higher-order moments, including the skewness $\gamma_1(R)$, excess kurtosis $\gamma_2(R)$ and the corresponding probability distribution function $P[N(R)]$ of a large family of models across the first three space dimensions, including both hyperuniform and nonhyperuniform models. Specifically, we derive explicit integral expressions for $\gamma_1(R)$ and $\gamma_2(R)$ involving up to three- and four-body correlation functions, respectively. We also derive rigorous bounds on $\gamma_1(R)$, $\gamma_2(R)$ and $P[N(R)]$. High-quality simulation data for these quantities are generated for each model. We also ascertain the proximity of $P[N(R)]$ to the normal distribution via a novel Gaussian distance metric $l_2(R)$. Among all models, the convergence to a central limit theorem (CLT) is generally fastest for the disordered hyperuniform processes. The convergence to a CLT is slower for standard nonhyperuniform models, and slowest for the antihyperuniform model studied here. We prove that one-dimensional hyperuniform systems of class I or any $d$-dimensional lattice cannot obey a CLT. Remarkably, we discovered that the gamma distribution provides a good approximation to $P[N(R)]$ for all models that obey a CLT, enabling us to estimate the large-$R$ scalings of $\gamma_1(R)$, $\gamma_2(R)$ and $l_2(R)$. For any $d$-dimensional model that "decorrelates" or "correlates" with $d$, we elucidate why $P[N(R)]$ increasingly moves toward or away from Gaussian-like behavior, respectively.

European option pricing using Gumbel distribution

A risk-neutral-density (RND) function plays a key role in determining option prices accurately. The RND function is useful in understanding the negative skewness and the excess kurtosis of the stock returns. RND models bases on the log-normal distribution (for example, Black–Scholes (BS) model (Black, F and M Scholes (1973). The pricing of options and corporate liabilities, The Journal of Political Economy 3, 637–654)) are less accurate to capture the negative skewness and the excess kurtosis of stock returns (Markose, S and A Alentorn (2011). The generalized extreme value distribution, implied tail index, and option pricing, The Journal of Derivatives 18(3), 35–60). The Extreme Value Theory (EVT) is useful in addressing the tail behavior of stock returns. The tail shape parameter in a Generalized Extreme Value (GEV) distribution class helps control tails’ size and shape. This paper model, the RND function in pricing the European call option, is modeled using a GEV distribution class, namely, a Gumbel distribution. It then compares GEV distribution option values with the BS values. It observes that the BS model underprices the call option values near maturity compared to those obtained by the GEV model. The Gumbel distribution for stock returns is useful in reducing the pricing bias of the BS model.

A Statistical Study on the Parameters of the Skew Normal Distribution Depending on the Use of the Genetic Algorithm Using the Simulation Method

Recent statistical research has witnessed activity on the study of skew normal distribution (SND) due to the fact that the data set does not fit well with the normal distribution due to Skewnessand excessive Kurtosis. For the purpose of estimating the parameters of the model (SND), the maximum likelihood method (ML) was used, but the probability equations of this method do not have clear solutions in the distribution (SND), and the problem was solved using the genetic algorithm (GA) and Other repetitive techniques are Newton Raphson, Nelder Mead and Iteratively Reweighting Algorithm, using the simulation method with different sample sizes and comparing the preference of results methods used based on criteria (Mean, Mse and Def). It has been concluded that (ML) capabilities using the (GA) of parameters (SND) are best in the case of a small or medium sample size and the best (IR) algorithm at a large sample size.

Testing P-Technique Factor Analysis With Non-Normal Time Series

There is an increasing need to analyze multivariate time series data due to the rapid development of data collection tools such as smartphone APPs, wearable sensors, and brain imaging techniques. P-technique factor analysis allows researchers to establish a measurement model for these time series. Analyzing such data is challenging because they are often non-normal (e.g., steps, heart rate, sleep, mood, and brain signals) and correlated at nearby time points. We propose using a bootstrap procedure to accommodate both the non-normality and the dependency of nearby time points. We explore the statistical properties with simulated data and illustrate the test with two empirical data sets. The results of the simulation study include (1) the bootstrap procedure performed better than an existing analytic procedure for time series data with excessive kurtosis (2) an existing analytic procedure performed better than the bootstrap procedure for normal time series and skewed time series.

Canadian industry level production and energy prices

Energy price volatility has a negative effect on economic activity in the United States, Canada and other countries. In this paper, we use disaggregated production data to examine which Canadian industries are most strongly affected by energy price volatility. We also generalize a heteroskedastic vector autoregression with a multivariate t distribution to account for excess kurtosis in conditional energy returns. We find that Canadian industries related to mining and extraction, manufacturing and transportation are most strongly affected by energy volatility; and that accounting for the excess kurtosis significantly improves the fit of the empirical model. We include several tests of robustness, including measures of energy volatility that incorporate stochastic volatility and asymmetries in the variance process. Our results suggest that uncertainty about energy prices reflects both macroeconomic uncertainty and uncertainty about energy markets.

Asymptotically valid Bayesian inference in the presence of distributional misspecification in VAR models

Inaccurately imposing Gaussian distributional assumptions in standard multivariate time series models does not affect inference on the autoregressive coefficients but distorts both classical and Bayesian inference on the volatility matrix whenever the true error distribution has excess kurtosis relative to the multivariate normal density. Inference on the intercept is also affected whenever the innovations are generated from a non-symmetric distribution. As a result of distributional misspecification, Bayesian methods lead to asymptotically invalid posterior inference for the intercept and the volatility matrix and, consequently, invalid posterior credible sets for quantities such as impulse responses, variance decompositions and density forecasts. We propose a robust and computationally fast Bayesian procedure which delivers asymptotically correct posterior credible sets without the need for distributional assumptions. The proposed corrected Bayesian posteriors for the volatility matrix and the intercept vector are based on the asymptotic covariance of the QML estimators and admit a closed form. Implementation of the procedure requires consistent estimation of the multivariate skewness and kurtosis of the innovations, and we propose novel shrinkage estimators designed to shrink these large dimensional objects towards the skewness and kurtosis of a Gaussian vector. We extend our robust Bayesian analysis to accommodate non-Gaussian disturbances in the presence of parameter instability, by combining the estimators of the current paper with semi-parametric kernel-type methods. We demonstrate that our estimators deliver correct posterior coverage rates in an extensive Monte Carlo exercise under a variety of distributional specifications. Finally, we present empirical evidence that imposing Gaussianity or homoskedasticity assumptions on financial and uncertainty shocks is not justified and may lead to misleading empirical conclusions.