THE RELATIONSHIPS BETWEEN SKEWNESS AND KURTOSIS

Centre-free kurtosis orderings for asymmetric distributions

The concept of kurtosis is used to describe and compare theoretical and empirical distributions in a multitude of applications. In this connection, it is commonly applied to asymmetric distributions. However, there is no rigorous mathematical foundation establishing what is meant by kurtosis of an asymmetric distribution and what is required to measure it properly. All corresponding proposals in the literature centre the comparison with respect to kurtosis around some measure of central location. Since this either disregards critical amounts of information or is too restrictive, we instead revisit a canonical approach that has barely received any attention in the literature. It reveals the non-transitivity of kurtosis orderings due to an intrinsic entanglement of kurtosis and skewness as the underlying problem. This is circumvented by restricting attention to sets of distributions with equal skewness, on which the proposed kurtosis ordering is shown to be transitive. Moreover, we introduce a functional that preserves this order for arbitrary asymmetric distributions. As application, we examine the families of Weibull and sinh-arcsinh distributions and show that the latter family exhibits a skewness-invariant kurtosis behaviour.

Signaleeg : A practical tool for EEG signal data mining

Due to the proliferation of brain and neurological disorders (World Health Organization 2006), EEG (Blinowska and Durka 2006) is gaining attention as a support for decision making in the fields of neurology, psychology, and psychiatry. But EEG data are not always easy to understand. Therefore, extracting the desired information from EEG data in different contexts is an important requirement. This article analyses state-of-the-art EEG signal processing tools and proposes a new one: Signaleeg. This addresses the limitations of previous tools. It has been designed with the aim of helping users to build predictive models from EEG signals in a process that is called signal-data mining (DM). Moreover, Signaleeg is user friendly and multi-threaded, with optimisation facilities for finding the best predictive model. It has been implemented and tested in three scenarios: schizophrenia diagnosis, alcoholism detection, and emotion recognition. The tool provided good results in each case, thus demonstrating its versatility.

Biometric Alterations of Mouse Embryonic Eye Structures Due to Short-Term Folic Acid Deficiency

PURPOSE

Folic acid (FA) is an essential nutrient for normal embryonic development. FA deficiency (FAD) in maternal diet increases the risk of several defects among the progeny, especially, neural tube defects. The eye begins its development from the neural tube; however, the relationship between FAD and ocular development in the offspring has been little explored and it isn't known how the FAD affects the formation of the eye. Our objective was to analyze the effect of maternal FAD on mouse embryos ocular biometry.

METHODS

Female mice C57/BL/6J were distributed into three different groups, according to the assigned diet: control group fed a standard FA diet (2 mg FA/kg), FAD group for short term fed (0 mg FA/kg + 1% succinylsulfathiazole) from the day after mating until day 14.5 of gestation, and FAD group for long term fed the same FA-deficient diet for 6 weeks prior mating and continued with this diet during gestation. A total of 57 embryos (19 embryos of each dietary group) at 14.5 gestational days were evaluated. As indicators of changes in ocular biometry, we analyze two parameters: area and circularity of the lens and whole eye, and the area of the retina. The program used in the treatment and selection of the areas of interest was ImageJ. The statistical analysis was performed by IBM SPSS Statistics 19.

RESULTS

Regarding the measures of the area, FA-deficient lenses and eyes were smaller than that of controls. We have also observed increase in the size of the neural retina, spatially, in embryos from females fed FAD diet during long term. On the other hand, as regard to circularity measures, we have seen that eyes and lenses were more circular than control.

CONCLUSION

Maternal FAD diet for a very short term generates morphological changes in ocular structures to the offspring.

Transition to collective oscillations in finite Kuramoto ensembles

We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this purpose, the minimal value of the amplitude of the complex Kuramoto order parameter appears as a proper indicator. The dependence of this minimum on coupling strength varies due to sampling variations and correlates with the sample kurtosis of the natural frequency distribution. The skewness of the frequency sample determines the frequency of the resulting collective mode. The effects of kurtosis and skewness hold in the thermodynamic limit of infinite ensembles. We prove this by integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively.

Decomposition of stock market trade-offs using Shewhart methodology

Purpose

The purpose of this paper is to investigate the applicability of Shewhart methodology and other quality management principles to gain a deeper understanding of the observed volatility in stock returns and its impact on market performance.

Design/methodology/approach

The validity of quality management philosophy in the context of financial market behaviour is discussed. The technique of rational subgrouping is used to identify the observable variations in stock returns as either common or special cause variation. The usefulness of the proposed methodology is investigated through empirical data. The risk/return and skewness/kurtosis trade-offs of S&P 500 stocks are examined. The consistency of this approach is reviewed by relating the separated variability to “efficient market” and “behavioural finance” theories.

Findings

Significant positive and negative risk/return trade-offs were found after partitioning the returns series into common and special cause periods, respectively, while total data did not exhibit a significant risk/return trade-off at all. A highly negative skewness/kurtosis trade-off was found in total and special cause periods as compared to the common cause periods. These results are broadly consistent with the theoretical concepts of finance and other empirical findings.

Practical implications

The quality management principles-based approach to analysing financial data avoids the complexities commonly found in stochastic-volatility forecasting models.

Social implications

The results provide new insights into the impact of volatility in stock returns. They should have direct implications for financial market participants.

Originality/value

The authors explore the relevance of Shewhart methodology in analysing variability in stock returns through reviewing financial market behaviour.