We point out that the quartic cumulant (and kurtosis) of the order parameter fluctuations is universally negative when the critical point is approached on the crossover side of the phase separation line. As a consequence, the kurtosis of a fluctuating observable, such as, e.g., proton multiplicity, may become smaller than the value given by independent Poisson statistics. We discuss implication...

In this communication, sample measures of kurtosis adapted by various software packages are compared for data from normal and non-normal populations. Further, two improved estimators of population kurtosis are proposed and their performance is compared with the currently used measures. The suggested estimators have considerably lower mean squared error (MSE) for various sampling designs in our ...

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...

This paper presents an original approach for blind deconvolution of a nonlinear communication channel using a criterion based on the secondand fourth-order moments of the input sequence. This approach is a simple extension of kurtosis maximization a method well known in a linear blind identification. We illustrate through a simple example that kurtosis maximization may also be used in a general...

This paper presents a new application of mathematical morphology (MM) operators for low speed slew bearing condition monitoring. The MM operators were used as a signal processing step and feature extraction method for bearing vibration signals. Four basic MM operators; erosion, dilation, closing and opening, were studied. This paper also investigates another potential MM operator, namely gradie...

This paper presents a theoretical analysis of the effect of constellation shaping in the transmitter on multimodulus (MMA) blind equalization in the receiver. Constellation shaping reduces average signal energy by a non-uniform distribution of constellation point utilization. Optimal transmit efficiency is achieved by a Gaussian distribution but many blind equalization algorithms require a non-...

Independent component analysis (ICA) solves the blind source separation problem by evaluating higher-order statistics, e.g. by estimating fourthorder moments. While estimation errors of the kurtosis can be shown to asymptotically decay with sample size according to a square-root law, they are subject to two further effects for finite samples. Firstly, errors in the estimation of kurtosis increa...

This paper has two-fold contribution. First, normality of the crop yield residuals are examined using panel statistical procedures accounting for trend, autocorrelation and heteroskedasticity. Second, to evaluate the importance of accounting for spatial and temporal variation on the normality of crop yield residuals, the changes in the skewness, kurtosis and D’Agostino-Pearson 2 (K ) omnibus no...

This paper proposes measures of systematic skewness and systematic kurtosis as symmetric measures of risk by extending the work of Kraus and Litzenberg (1976). We examine an asset pricing model that incorporates systematic skewness and systematic kurtosis to test the cross section of asset returns within the context of the Fama and MacBeth (1973) two-pass estimation methodology. However, this e...

We discuss the real-space moments of temperature anisotropies in the cosmic microwave background ~CMB! due to weak gravitational lensing by intervening large-scale structure. We show that if the probability distribution function of primordial temperature anisotropies is Gaussian, then it remains unchanged after gravitational lensing. With finite resolution, however, nonzero higher-order cumulan...