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Yilmaz et al. (Fluct. Noise Lett. 17, 1830002, 2018) investigated the stochastic phenomenological bifurcations of a generalized Chua circuit driven by Skew-Gaussian distributed noise. They proved it is possible to decrease the number of scrolls by properly choosing the stochastic excitation, manipulating the skewness and noise intensity parameters. Based on the latter, this paper proposes an extension of skew-gaussian noise based on the family of Scale Mixtures of Skew-normal (SMSN) distributions, which includes the skew- t , the skew-gaussian, and the gaussian noises as particular cases. The Lorenz, Generalized Lorenz, Proto–Lorenzand Rossler attractors driven by skew- t distributed noise are considered. Results show that the chaotic regime’s behavior is influenced by the freedom parameter degrees of skew- t noise, increasing the noise variance. This paper concludes that noise intensity increases by rescaling the skew- t distribution at zero mean, rather than by increasing the asymmetry parameter.

We investigated the relationship between environmental variables and the Gonadosomatic Monthly Mean (GMM) index of anchovy ( Engraulis ringens ) to understand how the environment affects the dynamics of anchovy reproductive timing. The data examined corresponds to biological information collected from samples of the landings off northern Chile (18°21′S, 24°00′S) during the period 1990–2010. We used the Humboldt Current Index (HCI) and the Multivariate ENSO Index (MEI), which combine several physical-oceanographic factors in the Tropical and South Pacific regions. Using the GMM index, we studied the dynamics of anchovy reproductive timing at different intervals of length, specifically females with a length between 11.5 and 14 cm (medium class) and longer than 14 cm (large class). Seasonal Autoregressive Integrated Mobile Average (SARIMA) was used to predict missing observations. The trends of the environment and reproductive indexes were explored via the Breaks For Additive Season and Trend (BFAST) statistical technique and the relationship between these indexes via cross-correlation functions (CCF) analysis. Our results showed that the habitat of anchovy switched from cool to warm condition, which also influenced gonad development. This was revealed by two and three significant changes (breaks) in the trend of the HCI and MEI indexes, and two significant breaks in the GMM of each time series of anchovy females (medium and large). Negative cross-correlation between the MEI index and GMM of medium and large class females was found, indicating that as the environment gets warmer (positive value of MEI) a decrease in the reproductive activity of anchovy can be expected. Correlation between the MEI index and larger females was stronger than with medium females. Additionally, our results indicate that the GMM index of anchovy for both length classes reaches two maximums per year; the first from August to September and the second from December to January. The intensity (maximum GMM values at rise point) of reproductive activity was not equal though, with the August–September peak being the highest. We also discuss how the synchronicity between environment and reproductive timing, the negative correlation found between MEI and GMM indexes, and the two increases per year of anchovy GMM relate to previous studies. Based on these findings we propose ways to advance in the understanding of how anchovy synchronize gonad development with the environment.

Fisher information is a measure to quantify information and estimate system-defining parameters. The scaling and uncertainty properties of this measure, linked with Shannon entropy, are useful to characterize signals through the Fisher–Shannon plane. In addition, several non-gaussian distributions have been exemplified, given that assuming gaussianity in evolving systems is unrealistic, and the derivation of distributions that addressed asymmetry and heavy–tails is more suitable. The latter has motivated studying Fisher information and the uncertainty principle for skew-gaussian random variables for this paper. We describe the skew-gaussian distribution effect on uncertainty principle, from which the Fisher information, the Shannon entropy power, and the Fisher divergence are derived. Results indicate that flexibility of skew-gaussian distribution with a shape parameter allows deriving explicit expressions of these measures and define a new Fisher–Shannon information plane. Performance of the proposed methodology is illustrated by numerical results and applications to condition factor time series.

In this paper we addressed the problem of backcasting and forecasting non-stationary time series. Given that traditional backcasting are based on the classical cross-correlation function assuming two stationary time series, assumptions based on two non-stationary time series need a new approach. Thus, Detrended Cross-Correlation Analysis (DCCA) provides a fanned estimator for a correlation between two non-stationary time series, providing then the stationary time series. Therefore, we developed a backcaster estimator and a predictor for the obtained stationary time series. The practical example of a Chilean cement production time series (1991–2015) illustrates our results.

In this paper, we provide the R\'enyi entropy and complexity measure for a novel, flexible class of skew-gaussian distributions and their related families, as a characteristic form of the skew-gaussian Shannon entropy. We give closed expressions considering a more general class of closed skew-gaussian distributions and the weighted moments estimation method. In addition, closed expressions of R\'enyi entropy are presented for extended skew-gaussian and truncated skew-gaussian distributions. Finally, additional inequalities for skew-gaussian and extended skew-gaussian R\'enyi and Shannon entropies are reported., Comment: 13 pages

The problem of measuring the disparity of a particular probability density function from a normal one has been addressed in several recent studies. The most used technique to deal with the problem has been exact expressions using information measures over particular distributions. In this paper, we consider a class of asymmetric distributions with a normal kernel, called Generalized Skew-Normal (GSN) distributions. We measure the degrees of disparity of these distributions from the normal distribution by using exact expressions for the GSN negentropy in terms of cumulants. Specifically, we focus on skew-normal and modified skew-normal distributions. Then, we establish the Kullback–Leibler divergences between each GSN distribution and the normal one in terms of their negentropies to develop hypothesis testing for normality. Finally, we apply this result to condition factor time series of anchovies off northern Chile.

Von Bertalanffy growth models (VBGMs) have been used in several studies of age, growth and natural mortality. Assuming that the residuals about this growth model are normal is, however, questionable. Here, we assume that these residuals are heteroskedastic and follow a log-skew-t distribution, a flexible distribution that is asymmetric and heavy-tailed. We apply the proposed methodology to length-at-age data for the southern blue whiting (Micromesistius australis) collected from Chilean austral continental waters between 1997 and 2010. The estimates of the VBGM parameters were L∞ = 57.042 cm, K = 0.173 yr−1, t0 = −2.423 yr for males, and L∞ = 61.318 cm, K = 0.163 yr−1, t0 = −2.253 yr for females. The BIC criteria suggest that females grow significantly faster than males and that length-at-age for both sexes exhibits significant heteroskedasticity and asymmetry.

Changes in phenology are an ecological response to climate changes, in addition to other factors that may stress or dampen phenological responses. For this study, we investigated how climate variability can affect the phenology of the reproductive process of the anchovy Engraulis ringens. We used 29 years of sea surface temperature (SST) data and biological information from northern Chile stock, particularly, gonadosomatic index (GI), body condition (K), and mean weight (MTW) between 1988 and 2017. The Breaks for Additive Season and Trend (BFAST) method was applied to SST to estimate seasonal breaks and to correlate them with the seasonality of the GI. Seasonality and trend were extracted from the series to evaluate them as co-variables in GAM and GLM models in the explanation of the GI variability. The GAM model explained 56% of the variance, because it rescues the nonlinear relationships of the variables. The seasonality of the temperature explained 40%, followed by the body condition of the fish (10%). BFAST results indicate a seasonal change in SST, recording three periods: prior to 1993, 1994–1998 and after 2009. This seasonal change in the SST determines a delay in the start and the maximum in the GI. The K presented a negative relationship such as the MTW, associated with energy expenditure during the reproductive period. Faced with projections of climate change, the effects of the decoupling between larvae and the abundance during spring are not known; therefore, knowing the mechanisms that control phenology can improve our capacity to monitor and manage marine resources under climate change.

An asymptotic expression for the Kullback–Leibler (KL) divergence measure of multivariate skew- t distributions (MST) is derived. This novel class of flexible family distributions incorporates a shape and degree of freedom parameters, in order to manipulate the skewness and heavy-tail presence of the data, respectively. The quadratic form expressions of MST models are used to provide asymptotic measures. Additional inequalities for MST entropy and simulation studies are reported. Finally, the expected values of the KL divergence of a sample correlation matrix obtained by Pearson’s correlation coefficient are discussed.

Our article presents a robust and flexible statistical model of the age–length relationship of cardinalfish ( Epigonus crassicaudus ). Specifically, we consider a non-linear regression model in which the error distribution allows for heteroskedasticity and belongs to the skew-normal (SMSN) distributions family of scale mixtures, thus eliminating the need to transform the dependent variable using techniques such as the Box–Cox transformation. The SMSN is a tractable and flexible class of asymmetric, heavy-tailed distributions that is useful for robust inference when the normality assumption for the error distribution is questionable. Two well-known important members of this class are the proper skew-normal and skew- t distributions. In this work, the skew- t model is emphasised. However, the proposed methodology can be adapted for each of the SMSN models with some basic changes. The present work is motivated by a previous analysis of cardinalfish where the oldest specimen was 15 years of age. In this study, we use the proposed methodology on a data set based on an otolith sample where the determined longevity is higher than 54 years.

The entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions. We study in detail the cases of the multivariate skew-normal and skew-t distributions. We implement our findings to the application of the optimal design of an ozone monitoring station network in Santiago de Chile.

Biological-fishery indicators have been widely studied. As such the condition factor (CF) index, which interprets the fatness level of a certain species based on length and weight, has been investigated, too. However, CF has been studied without considering its temporal features and distribution. In this paper, we analyze the CF time series via skew-gaussian distributions that consider the asymmetry produced by extreme events. This index is characterized by a threshold autoregressive model and corresponds to a stationary process depending on the shape parameter of the skew-gaussian distribution. Then we use the Jensen–Shannon (JS) distance to compare CF by length classes. This distance has mathematical advantages over other divergences such as Kullback–Leibler and Jeffrey’s, and the triangular inequality property. Our results are applied to a biological catalogue of anchovy (Engraulis ringens) from the northern coast of Chile, for the period 1990–2010 that consider monthly CF time series by length classes and sex. We find that for high values of shape parameter, JS distance tends to be more sensible to detect discrepancies than Jeffrey’s divergence. In addition, the body condition of male anchovies with higher lengths coincides with the ending of the moderate-strong El Niño event 91–92 and for both males and females, the smaller lengths coincide with the beginning of the strong El Niño event 97–98.

The aim of this work is to provide the tools to compute the well-known Kullback–Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these distributions. Finally, we applied our results on a seismological catalogue data set related to the 2010 Maule earthquake. Specifically, we compare the distributions of the local magnitudes of the regions formed by the aftershocks.