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This paper explores bimodal skew-symmetric distributions, a versatile family of distributions characterized by parameters that control asymmetry and kurtosis. These distributions encapsulate both symmetrical and well-known asymmetrical behaviors. A simulation study evaluates the model's estimation accuracy, detailing the score function and the robustness of the observed information matrix, which is proven to be non-singular under specific conditions. We apply the bimodal skew-normal model to protein data from cancer cells, comparing its performance against four established distributions supported on the entire real line. Results indicate superior performance by the proposed model, underscoring its potential for enhancing analytical precision in biological research. [ABSTRACT FROM AUTHOR]

A flexible distribution has been introduced to handle random variables in the unit interval. This distribution is based on an exponential transformation of the truncated positive normal distribution with two parameters and can effectively fit data with varying degrees of skewness and kurtosis. Therefore, it presents an alternative for modeling this type of data. Several mathematical and statistical properties of this distribution have been derived, such as moments, hazard function, the Bonferroni curve, and entropy. Moreover, we investigate the characterizations of the proposed distribution based on its hazard function. Parameter estimation has been performed using both the maximum likelihood method and method of the moments. Because of this, we were able to determine the best critical region and the information matrix, facilitating the calculation of asymptotic confidence intervals. A simulation study is presented to analyze the behavior of the obtained estimators for different sample sizes. To demonstrate the suitability of the proposed distribution, applications and goodness-of-fit tests have been performed on two practical data sets. [ABSTRACT FROM AUTHOR]

Using a two-piece normal distribution for modeling univariate data that exhibits symmetry, and uni/bimodality is notably effective. In this respect, the shape parameter value determines whether unimodality or bimodality is present. This paper proposes a flexible uni/bimodal distribution with platykurtic density, which can be used to simulate a variety of data. The concept is based on the transforming of a random variable into a folded distribution. Further, the proposed class includes the normal distribution as a sub-model. In the current study, the maximum likelihood method is considered for deriving the main structural properties and for the estimation of parameters. In addition, simulation experiments are presented to evaluate the behavior of estimators. Finally, fitting and regression applications are presented to illustrate the usefulness of the proposed distribution for data modeling in different real-life scenarios. [ABSTRACT FROM AUTHOR]

Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. We propose a novel estimation procedure of stress–strength reliability in the case of two independent unit-half-normal distributions can fit asymmetrical data with either positive or negative skew, with different shape parameters. We obtain the maximum likelihood estimator of the reliability, its asymptotic distribution, and exact and asymptotic confidence intervals. In addition, confidence intervals of model parameters are constructed by using bootstrap techniques. We study the performance of the estimators based on Monte Carlo simulations, the mean squared error, average bias and length, and coverage probabilities. Finally, we apply the proposed reliability model in data analysis of burr measurements on the iron sheets. [ABSTRACT FROM AUTHOR]

Recent years have shown growth in the potential applications of extensions of skew and half-normal distributions. In this paper, we provide and study, in detail, an extended class of such distributions. The presented distribution has a scale parameter and two shape parameters. The motivations behind the development of this distribution are: 1- the probability distribution function has skewed, unimodal and bathtub shapes with different styles and the hazard rate function is increasing with various shapes, which makes this distribution flexible enough to analyze reliability data; 2- it can be expressed as a mixture of the Generalized Half-Normal distribution and the new weighted Generalized Half-Normal distribution. A number of statistical results are derived. Monte Carlo simulation analysis is carried out withMaximum Likelihood Estimation to assess the performance of this technique for a variety of the distribution parameter values. The power of the distribution is demonstrated with real applications using two reliability datasets from the industry. The results reveal that the proposed distribution outperformed the Generalized Lindley, Exponentiated Exponential, Gamma, Alpha-Skew-Normal, the Half-Alpha-Skew-Normal, and the Modified Generalized Half-Normal distributions. [ABSTRACT FROM AUTHOR]

In this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

In [Martínez-Flórez G, Bolfarine H, Gómez HW. Skew-normal alpha-power model. Statistics. 2014;48(6):1414-1428] the authors make an error in calculating the information matrix of the skew-normal alpha-power model under the normality hypothesis . Here we prove that the information matrix under is singular and we proposed a reparametrization that allows one to calculate the asymptotic distribution of the maximum likelihood estimator. [ABSTRACT FROM AUTHOR]

This paper focuses on the development of a new extension of the generalized skew-normal distribution introduced in Gómez et al. [Generalized skew-normal models: properties and inference. Statistics. 2006;40(6):495–505]. To produce the generalization a new parameter is introduced, the signal of which has the flexibility of yielding unimodal as well as bimodal distributions. We study its properties, derive a stochastic representation and state some expressions that facilitate moments derivation. Maximum likelihood is implemented via the EM algorithm which is based on the stochastic representation derived. We show that the Fisher information matrix is singular and discuss ways of getting round this problem. An illustration using real data reveals that the model can capture well special data features such as bimodality and asymmetry. [ABSTRACT FROM PUBLISHER]

Sun exposure is a major threat to the survival of cacti seeds in desertic environments. During summer, fruits of the columnar cactus Pachycereus pringlei from San Esteban Island, northwestern Mexico, are eaten by herbivorous iguanas, and after digestion, seeds are deposited within their scats. We compared the germination percentage of wild seeds exposed to the sun while lying on the ground of the island, with that of seeds collected directly from the fruit, and seeds obtained from old and recently deposited iguana scats. Our results indicate that direct sun exposure causes drastic reduction in seed germination, and this negative effect is reduced in seeds shielded inside feces, although with a cost on germination. We discuss some of the possible implications of seed shielding in the population of P. pringlei. • Elevated ground temperature causes seedling mortality. • P. pringlei seeds are consumed and dispersed by two herbivorous iguanas. • Gut-passage of the seeds causes a reduction in germination percentage. • Seeds are shielded from the high temperatures when inside the iguana's feces. • Seed shielding benefits depend on a trade-off dependent on the soil temperature. [ABSTRACT FROM AUTHOR]

Regression analysis is a technique widely used in different areas of human knowledge, with distinct distributions for the error term. It is the case, however, that regression models with the error term following a bimodal distribution are not common in the literature, perhaps due to the lack of simple to deal with bimodal error distributions. In this paper, we propose a simple to deal with bimodal regression model with a symmetric-asymmetric distribution for the error term for which for some values of the shape parameter it can be bimodal. This new distribution contains the normal and skew-normal as special cases. A real data application reveals that the new model can be extremely useful in such situations. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new distribution for modeling positive data with high kurtosis. This distribution can be seen as an extension of the exponentiated Rayleigh distribution. This extension builds on the quotient of two independent random variables, one exponentiated Rayleigh in the numerator and Beta (q; 1) in the denominator with q > 0 . It is called the slashed exponentiated Rayleigh random variable. There is evidence that the distribution of this new variable can be more flexible in terms of modeling the kurtosis regarding the exponentiated Rayleigh distribution. The properties of this distribution are studied and the parameter estimates are calculated using the maximum likelihood method. An application with real data re- veals good performance of this new distribution. [ABSTRACT FROM AUTHOR]

The Fisher information matrix for Generalized skew-normal (GSN) distribution is derived. The expressions for the elements of the matrices require of integrals that are solved numerically using a suitable software. [ABSTRACT FROM AUTHOR]

The aim of this study was to assess the relative importance of phytomer organogenesis, mortality, and elongation rates on the rhizome length of Eelgrass (Zostera marina). Rhizome length has both a discrete and a continuous component, which are the number of internodes and their lengths, respectively. We hypothesize that rhizome length would be more correlated with elongation rates than either phytomer organogenesis or mortality. An individual-based model was used to simulate the growth of Z. marina individuals in the Punta Banda estuary in Baja California, a low-latitude Eelgrass population. Individuals of the model were composed of a rhizome and lateral branches, both of which were composed of phytomers. The individuals changed by presenting horizontal growth, clonal reproduction, aging, and age-related mortality. Some growth rates were modeled with respect to environmental conditions. The model was validated by comparing the rhizome length of simulated and observed plants. A sensitivity analysis suggested that simulated rhizome length is most correlated to elongation rates, which are mainly affected by water temperature and irradiance. [Display omitted] • We model eelgrass rhizomes as composed of phytomers, each with an internode length. • Phytomer length was related to water temperature, light, and desiccation. • Organogenesis was not related to environmental conditions. • The length of simulated rhizomes is most affected by phytomer elongation rates. [ABSTRACT FROM AUTHOR]

This article proposes new symmetric and asymmetric distributions applying methods analogous as the ones in Kim (2005) and Arnold et al. (2009) to the exponentiated normal distribution studied in Durrans (1992), that we call the power-normal (PN) distribution. The proposed bimodal extension, the main focus of the paper, is called the bimodal power-normal model and is denoted byBPN(α) model, where α is the asymmetry parameter. The authors give some properties including moments and maximum likelihood estimation. Two important features of the model proposed is that its normalizing constant has closed and simple form and that the Fisher information matrix is nonsingular, guaranteeing large sample properties of the maximum likelihood estimators. Finally, simulation studies and real applications reveal that the proposed model can perform well in both situations. [ABSTRACT FROM AUTHOR]

The Andean Altiplano has served as a complex setting throughout its history, driving dynamic processes of diversification in several taxa. We investigated phylogeographic processes in the Telmatobius marmoratus species complex occurring in this region by studying the geographic patterns of genetic variability, genealogies, and historical migration, using the cytochrome b (cyt-b) gene as a marker. DNA sequences from Telmatobius gigas and Telmatobius culeus, Bolivian species with an uncertain taxonomic status, were also included. Additionally, we evaluated the phylogenetic diversity (PD) represented within Chilean protected areas and the complementary contribution from unprotected populations. Phylogenetic reconstructions from 148 cyt-b sequences revealed 4 main clades, one of which corresponded to T. culeus. T. gigas was part of T. marmoratus clade indicating paraphyletic relationships. Haplotypes from Chilean and Bolivian sites were not reciprocally monophyletic. Geographic distribution of lineages, spatial Bayesian analysis, and migration patterns indicated that T. marmoratus displays a weaker geographic structure than expected based on habitat distribution and physiological requirements. Demographic and statistical phylogeography analyses pointed out to a scenario of recent population expansion and high connectivity events of a more recent age than the post Last Glacial Maximum, probably associated to more humid events in Altiplano. PD of T. marmoratus populations within protected areas represents 55.6% of the total estimated PD. The unprotected populations that would contribute the most to PD are Caquena and Quebe (21%). Recent evolutionary processes and paleoclimatic changes, potentially driving shifts in habitat connectivity levels and population sizes, could explain the phylogeographic patterns recovered herein. [ABSTRACT FROM AUTHOR]

We consider a distribution obtained by combining two well-known mechanisms for generating skewed distributions. In this manner we arrive at a flexible model which subsumes and extends several skew distributions which have been discussed in the literature. One approach to the problem of generating skewed distributions was first popularized by Azzalini [A class of distributions which includes the normal ones. Scand J Stat. 1985;12:171–178]. The single constraint skew normal distribution that was studied by Azzalini is of the formwhere φ and Φ denote, respectively, the standard normal density and distribution function and α∈ℝ is a skewing parameter. Multiple constraint variations of this distribution have also been considered. The second skewing approach that we will consider was proposed by Mudholkar and Hutson [The epsilon-skew-normal distribution for analyzing near-normal data. J Statist Plann Inference. 2000;83:291–309] and called an epsilon-skew-normal distribution. The combination of an Azzalini mechanism with that of Mudholkar and Hutson is investigated in this paper with special focus on the distributions obtained using the standard normal as the base distribution. The resulting flexible model includes both unimodal and bimodal cases and can be expected to fit a wider variety of data configurations than either of the models involving a single skewing mechanism. Distributional and inferential properties of the doubly skewed model are discussed and the model is used to obtain improved fits to two well-known data sets. [ABSTRACT FROM AUTHOR]

A new class of unimodal asymmetric distributions is introduced to the unit interval and these distributions are useful for modeling data of percentages, proportions and fractions. Therefore, we propose the unit-half-normal distribution as a contribution to the earlier path and investigate some of its mathematical properties. The maximum likelihood estimator is obtained with a comprehensive inference. This new class of distributions belongs to the exponential family, hence the uniformly minimum variance unbiased estimator of the distribution parameter is obtained. The distribution represents a power alternative to the unit interval distributions, namely the beta, Kumaraswamy and other recent ones. We investigate a small simulation study to analyze the behavior of the obtained estimators for different sample sizes. Moreover, we illustrate the goodness of fit of the proposed model for image data. Lastly, we describe a procedure of incorporating covariates into regression analysis of the proposed distribution. [ABSTRACT FROM AUTHOR]

Chile has experienced a strong drought, which has been sustained since 2010. In this context, we conducted a trophic study for Lycalopex culpaeus, in the Chilean Mediterranean area, during this extreme climatic event to analyze how this phenomenon of restriction in the availability of trophic resources affects the diet of these foxes. The analysis of feces allows us to observe that L. culpaeus based its diet on lagomorphs and on the use of cattle, probably dead. During the study there was no change in foxes activity. Another interesting aspect was the sustained presence of carnivorous mammals in the feces throughout the year; the latter supports what has been observed in other regions, in that interspecific kills are common among carnivorous mammals. [ABSTRACT FROM AUTHOR]

The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution, we extend the univariate power-normal distribution to the multivariate setup. Structural properties of the new multivariate distributions are established. We consider the maximum likelihood method to estimate the unknown parameters, and the observed and expected Fisher information matrices are also derived. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

The Andean Altiplano has served as a complex setting throughout its history, driving dynamic processes of diversification in several taxa. We investigated phylogeographic processes in the Telmatobius marmoratus species complex occurring in this region by studying the geographic patterns of genetic variability, genealogies, and historical migration, using the cytochrome b (cyt-b) gene as a marker. DNA sequences from Telmatobius gigas and Telmatobius culeus, Bolivian species with an uncertain taxonomic status, were also included. Additionally, we evaluated the phylogenetic diversity (PD) represented within Chilean protected areas and the complementary contribution from unprotected populations. Phylogenetic reconstructions from 148 cyt-b sequences revealed 4 main clades, one of which corresponded to T. culeus. T. gigas was part of T. marmoratus clade indicating paraphyletic relationships. Haplotypes from Chilean and Bolivian sites were not reciprocally monophyletic. Geographic distribution of lineages, spatial Bayesian analysis, and migration patterns indicated that T. marmoratus displays a weaker geographic structure than expected based on habitat distribution and physiological requirements. Demographic and statistical phylogeography analyses pointed out to a scenario of recent population expansion and high connectivity events of a more recent age than the post Last Glacial Maximum, probably associated to more humid events in Altiplano. PD of T. marmoratus populations within protected areas represents 55.6% of the total estimated PD. The unprotected populations that would contribute the most to PD are Caquena and Quebe (21%). Recent evolutionary processes and paleoclimatic changes, potentially driving shifts in habitat connectivity levels and population sizes, could explain the phylogeographic patterns recovered herein. [ABSTRACT FROM AUTHOR]

The amphibian genus Telmatobius is a diverse group of species that inhabits the Andes. This study analysed the phylogenetic relationships of 19 species described from the central Andes of Chile and Bolivia, and 12 undescribed populations of Chile. A molecular phylogeny based on mitochondrial DNA 16S and cytochrome b shows that the Chilean species belong to three groups: (1) the Telmatobius marmoratus group, widespread in the Chilean and Bolivian Altiplano; (2) the Telmatobius hintoni group, including the species Telmatobius philippii, Telmatobius fronteriensis, and Telmatobius huayra, occurring in the south-western Altiplano of Chile and Bolivia, and (3) the Telmatobius zapahuirensis group, a new clade which also includes Telmatobius chusmisensis, Telmatobius dankoi, and Telmatobius vilamensis, restricted to western slopes of the Andes, and which was recovered as more closely related to the T. hintoni group than the T. marmoratus group. The divergence times between clades were traced to the late Pleistocene. The molecular phylogeny also confirmed that the groups of the Altiplano and western Andes slopes form a clade separated from the species that inhabit the eastern Andes ( Telmatobius verrucosus and Telmatobius bolivianus groups), supporting the forest origin of the Altiplano groups proposed by several previous authors. © 2014 The Linnean Society of London [ABSTRACT FROM AUTHOR]