Javier E. Contreras-Reyes

Kullback–Leibler Divergence Measure for Multivariate Skew-Normal Distributions

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.

Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

Our article presents a robust and flexible statistical modeling for the growth curve associated to the age-length relationship of Cardinalfish (Epigonus Crassicaudus). Specifically, we consider a non-linear regression model, in which the error distribution allows heteroscedasticity and belongs to the family of scale mixture of the skewnormal (SMSN) distributions, thus eliminating the need to transform the dependent variable into many data sets. The SMSN is a tractable and flexible class of asymmetric heavy-tailed distributions that are useful for robust inference when the normality assumption for error distribution is questionable. Two well-known important members of this class are the proper skew-normal and skew-t distributions. In this work emphasis is given to the skew-t model. However, the proposed methodology can be adapted for each of the SMSN models with some basic changes. The present work is motivated by previous analysis about of Cardinalfish age, in which a maximum age of 15 years has been determined. Therefore, in this study we carry out the mentioned methodology over a data set that include a long-range of ages based on an otolith sample where the determined longevity is higher than 54 years.

Statistical analysis of autoregressive fractionally integrated moving average models in R

The autoregressive fractionally integrated moving average (ARFIMA) processes are one of the best-known classes of long-memory models. In the package afmtools for R, we have implemented a number of statistical tools for analyzing ARFIMA models. In particular, this package contains functions for parameter estimation, exact autocovariance calculation, predictive ability testing and impulse response function computation, among others. Furthermore, the implemented methods are illustrated with applications to real-life time series.

Analyzing Fish Condition Factor Index Through Skew-Gaussian Information Theory Quantifiers

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 Nino event 91–92 and for both males and females, the smaller lengths coincide with the beginning of the strong El Nino event 97–98.

Rényi entropy and complexity measure for skew-gaussian distributions and related families

In this paper, we provide the Renyi 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 Renyi entropy are presented for extended skew-gaussian and truncated skew-gaussian distributions. Finally, additional inequalities for skew-gaussian and extended skew-gaussian Renyi and Shannon entropies are reported.

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

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.

Bounds on Rényi and Shannon Entropies for Finite Mixtures of Multivariate Skew-Normal Distributions: Application to Swordfish (Xiphias gladius Linnaeus)

Mixture models are in high demand for machine-learning analysis due to their computational tractability, and because they serve as a good approximation for continuous densities. Predominantly, entropy applications have been developed in the context of a mixture of normal densities. In this paper, we consider a novel class of skew-normal mixture models, whose components capture skewness due to their flexibility. We find upper and lower bounds for Shannon and Renyi entropies for this model. Using such a pair of bounds, a confidence interval for the approximate entropy value can be calculated. In addition, an asymptotic expression for Renyi entropy by Stirling’s approximation is given, and upper and lower bounds are reported using multinomial coefficients and some properties and inequalities of L p metric spaces. Simulation studies are then applied to a swordfish (Xiphias gladius Linnaeus) length dataset.

The Skew-Reflected-Gompertz distribution for analyzing symmetric and asymmetric data

Abstract In this work, we have defined a new family of skew distribution: the Skew-Reflected-Gompertz. We have also derived some of its probabilistic and inferential properties. The maximum likelihood estimates of the proposed distribution parameters are obtained via an EM-algorithm, and performances of the proposed model and its estimates are shown via simulation studies as well as real applications. Three real datasets are also used to illustrate the model performance which can compete against some well-known skew distributions frequently used in applications.

Incorporating uncertainty into a length-based estimator of natural mortality in fish populations

The views and opinions expressed or implied in this article are those of the author (or authors) and do not necessarily reflect the position of the National Marine Fisheries Service, NOAA. Abstract—Natural mortality (M) is one of the most important life history attributes of functioning fish populations. The most common methods to estimate M in fish populations provide point estimates which are usually constant across sizes and ages. In this article, we propose a framework for incorporating uncertainty into the length-based estimator of mortality that is based on von Bertalanffy growth function (VBGF) parameters determined with Bayesian analysis and asymmetric error distributions. Two methods to incorporate uncertainty in M estimates are evaluated. First, we use Markov chains of the estimated VBGF parameters directly when computing M and second, we simulate the posterior distribution of VBGF parameters with the copula method. These 2 approaches were applied and compared by using the extensive database available on age and growth for southern blue whiting (Micromesistius australis) harvested in the southeast Pacific. The copula approach provides advantages over Markov chains and requires far less computational time, while conserving the underlying dependence structure in the posterior distribution of the VBGF parameters. The incorporation of uncertainty into length-based estimates of mortality provides a promising way for modeling fish population dynamics. Natural mortality (M) rate is one of the most important parameters shaping the population dynamics of fish populations (Siegfried and Sansó1; Brodziak et al., 2011). It is defined as the death rate of fish due to causes other than fishing, such as predation, senescence, cannibalism, starvation, and other natural factors. Despite the key importance of M in fish and fisheries modeling, this parameter is extraordinarily difficult to estimate accurately. Methods for determining M in fish populations generally entail one of 2 approaches: 1) direct methods which estimate M from observations on survival, with methods derived from tagging or telemetry experiments, 2) indirect methods that estimate mortality from other, more easily obtained parameters, often from life history traits, such as age and growth, and maturity. Direct methods provide the most precise estimates of M, but those approaches

Credit allocation based on journal impact factor and coauthorship contribution

Some research institutions demand researchers to distribute the incomes they earn from publishing papers to their researchers and/or co-authors. In this study, we deal with the Impact Factor-based ranking journal as a criteria for the correct distribution of these incomes. We also include the Authorship Credit factor for distribution of the incomes among authors, using the geometric progression of Cantors theory and the Harmonic Credit Index. Depending on the ranking of the journal, the proposed model develops a proper publication credit allocation among all authors. Moreover, our tool can be deployed in the evaluation of an institution for a funding program, as well as calculating the amounts necessary to incentivize research among personnel.