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We introduce a parameterization for the multivariate skew normal and skew-t distributions, which enforces an orthogonal structure on the skewness parameter. This approach provides substantial benefits in computational efficiency during parameter estimation, resulting in a model which strikes an excellent balance between flexibility and model-fitting feasibility. We illustrate this primarily through implementing the proposed distributions in a mixture model-based clustering framework. We compare to competing skew distributions via both simulated and real data analyses, reporting both computation time and model-fit metrics. [ABSTRACT FROM AUTHOR]

Gaussian mixture models, which assume a Normal distribution for each component, are popular in antibody (or serological) data analysis to help determining antibody-positive and antibody-negative individuals. In this work, we advocate using finite mixture models based on Skew-Normal and Skew-t distributions for serological data analysis. These flexible mixing distributions have the advantage of describing right and left asymmetry often observed in the distributions of known antibody-negative and antibody-positive individuals, respectively. We illustrate the application of these alternative mixture models in a data set on the role of human herpesviruses in the Myalgic Encephalomyelitis/Chronic Fatigue Syndrome.

ایران کشور است که هرساله با طوفان­های تندری زیادی روبه­رو است. لذا در پژوهش حاضر به توزیع زمانی و مکانی و همچنین واکاوی همدیدی و ترمودینامیکی وقوع طوفان­های تندری در بخش وسیعی از فلات ایران پرداخته‌ شد. بدین منظور از داده­های مربوط به‌روزهای همراه با طوفان تندری، 20 ایستگاه همدید در فلات ایران با تأکید بر نیمه شرقی کشور و همچنین داده‌های ارتفاع ژئوپتانسیل (hgt)، امگا (Omega) و رطوبت ویژه (Shum) در طول دوره آماری 2010 تا 2015 استفاده شد. پس از استخراج روزهای همراه با طوفان تندری، با استفاده از نرم‌افزار GIS Arc و روش IDW نقشه­های توزیع زمانی و مکانی تهیه گردید. سپس با استفاده از نرم‌افزار GrADS نقشه­های همدیدی لازم در ترازهای مختلف جو تهیه و تحلیل گردید. بررسی­های ترمودینامیکی نیز با استفاده از نمودارهای Skew-t و شاخص­های CAPE و PWAT انجام شد. نتایج حاصل از توزیع زمانی و مکانی نشان داد که در مقیاس ماهانه، از ایستگاه جیرفت در استان کرمان به سمت عرض­های بالا در ماه­های آوریل و می، بیشترین فراوانی طوفان تندری وجود داشته و به‌طرف عرض­های پایین­تر از ماه دسامبر تا فوریه فراوانی طوفان­های تندری بیشتر می­گردد. در مقیاس فصلی نیز در نیمه شمالی منطقه موردمطالعه بیشترین رخداد طوفان­های تندری در فصل بهار دیده می­شود؛ درحالی‌که در نیمه جنوبی بیشترین فراوانی مربوط به فصل زمستان است. درمجموع در همه مناطق موردمطالعه در طول سال کم­و­بیش پتانسیل رخداد طوفان تندری وجود دارد. نتایج حاصل از واکاوی همدیدی نیز نشان داد که در روزهای همراه با طوفان تندری، اُمگای منفی و صعود و ناپایدار هوا حاکم بوده و از سوی دیگر، نفوذ رطوبت به جو منطقه و قرارگیری در زیر سرد چال‌ها و جلوی ناوه، شرایط را برای رخداد این پدیده فراهم می­کند. بررسی نمودارهای skew-t و شاخص­های CAPE و PWAT نیز بیانگر وجود رطوبت بیشتر در روز طوفان نسبت به‌روز قبل از طوفان و ناپایداری ناشی از صعود همرفتی شدید (حدود دو برابر) در روز رخداد طوفان تندری است.

This article proposes a new class of Real Elliptically Skewed (RESK) distributions and associated clustering algorithms that integrate robustness and skewness into a single unified cluster analysis framework. Non-symmetrically distributed and heavy-tailed data clusters have been reported in a variety of real-world applications. Robustness is essential because a few outlying observations can severely obscure the cluster structure. The RESK distributions are a generalization of the Real Elliptically Symmetric (RES) distributions. To estimate the cluster parameters and memberships, we derive an expectation maximization (EM) algorithm for arbitrary RESK distributions. Special attention is given to a new robust skew-Huber M-estimator, which is also the approximate maximum likelihood estimator (MLE) for the skew-Huber distribution, that belongs to the RESK class. Numerical experiments on simulated and real-world data confirm the usefulness of the proposed methods for skewed and heavy-tailed data sets. [ABSTRACT FROM AUTHOR]

Purpose: In this paper, we propose a robust Bayesian method for the assessment of average bioequivalence based on data from conventional crossover studies. We evaluate and motivate empirically the need for robust methods in bioequivalence studies by comparing the results of robust and conventional statistical methods in a large data pool of bioequivalence studies. Methods: Robustness of the statistical methodology is achieved by replacing the normal distributions for residuals in the linear mixed model with skew-t distributions. In this way, the statistical model can accommodate skew and heavy-tailed data, particularly outliers, yielding robust statistical inference without the need for excluding outliers from the analysis. We performed a simulation study to investigate and compare the performance of the robust and conventional models. Results: Our study shows that in some trials, the distribution of residuals is skew and heavy-tailed. In the presence of outliers, the 90% confidence intervals for the ratio of geometric means tend to be narrower for the robust methods than for the conventional method. Our simulation study shows that the robust method has suitable frequentist properties and yields more precise confidence intervals and higher statistical power than the conventional maximum likelihood method when outliers are present in the data. Conclusions: As a sensitivity analysis, we recommend the fit of robust models for handling outliers that are occasionally encountered in crossover design bioequivalence data. [ABSTRACT FROM AUTHOR]

Iran is a country that is faced with storms, thunderstorms, hail and floods every year. Therefore, in the present study, the temporal and spatial distribution and synoptic and thermodynamic analysis of the thunder storm occurrence in a large part of the Iran have been addressed. For this purpose, the data related to days with a thunderstorm of 20 synoptic stations in the eastern part of the Iran and geopotential heights (hgt), omega and specific moisture content (shum) data were used during the statistical period (2010-2015). After extraction of days with thunderstorms, ArcGIS software and IDW method were used for the temporal and spatial distribution maps. Then, using GrADS software synoptic maps were prepared and analyzed for different levels of atmosphere. Also, for the thermodynamic analysis, the Skew-t charts and CAPE and PWAT indices were used. The results of the temporal and spatial distribution have showed that from Jiroft city in the province of Kerman to the high latitudes in April and May, the highest frequency of thunder storms is observed and to the lower latitudes from December to February, there are a lot of thunder storms. In the northern part of the study area, the most frequent occurrence is in the spring and in the southern part of the region, the most occurrences occur in the winter. In total, in all the study areas throughout the year, there is shortly thunderstorm event. The results of the synoptic analysis also showed that during the days with thunderstorms, the negative omega and the ascending and unstable air, and on the other hand, the influence of moisture on the atmosphere of the area and the placement under the cut of low and the front of the Trough, conditions for the occurrence of this Provides a phenomenon. Investigating the skew-t charts and the CAPE and PWAT indices also indicate that there is more humidity in storm day than the day before the storm and the instability resulting from a severe convective rise (about twice) on the day of thunderstorm. [ABSTRACT FROM AUTHOR]

One of the most important environmental problems in recent years in the Middle East including Iran is the dust storm events. The main goal of this research was to conduct statistical analyses to identify the dusty days with visibility to less than 1 km. This study also dealt with the recognition of sources of this phenomenon and the route for dusts to enter Isfahan Province. In this study, data were collected for a 20-year period (1994–2013) including daily dust data at the ground stations, brightness temperature at wavelengths of 11 μm and 12 μm, and GDAS data for tracking the dust particle route in HYSPLIT software. Naein and Airport stations with frequencies of 920 and 919 days of dust (respectively) were identified as two critical centers of dust in Isfahan province. The spring season had the highest number of days with dust. Also, the highest and lowest frequencies of this event were observed in April–May–June and December–January, respectively. The border area between Iraq and Syria, west and southwest of Iraq, was the main source of the dust transported to Isfahan. Thermodynamic conditions of atmosphere using the Skew-T diagrams were stable during the dust events in the study area. [ABSTRACT FROM AUTHOR]

Rank-based analysis of linear models is based on selecting an appropriate score function. The information about the shape of the underlying distribution is necessary for the optimal selection; leading towards asymptotically efficient analysis. In this study, we analyzed the multilevel model with cluster-correlated error terms following a family of skew-t distribution with the rank-based approach based on score function derived for the class of skewnormal distribution. The rank fit is compared with the Restricted Maximum Likelihood (REML) estimation in terms of validity and efficiency for different sample sizes. A Monte Carlo simulation study is carried out over skewed-t and contaminated-t distribution with a range of skewness parameter from moderately to highly skewed. The standard error of regression coefficients is significantly reduced in the rank-based approach and further reduces for a large sample size. Rank-based fit appeared asymptotically efficient than REML for each shape parameter of skewness in skew-t and contaminated-t distribution computed through a calculation of precision. The empirical validity of fixed effects is obtained up to the nominal level 0.95 in REML but not rank-based with skew-normal score function. [ABSTRACT FROM AUTHOR]

This contribution describes a Decision Tree intended to guide the selection of statistical models and data reduction procedures in key comparisons (KCs). The Decision Tree addresses a specific need of the Inorganic Analysis Working Group (IAWG) of the Consultative Committee (CC) for Amount of Substance, Metrology in Chemistry and Biology (CCQM), of the International Committee for Weights and Measures (CIPM), and it is likely to address similar needs of other working groups and consultative committees. Because the portfolio of KCs previously organized by the CCQM-IAWG affords a full range of opportunities to demonstrate the capabilities of the Decision Tree, the majority of the illustrative examples of application of the Decision Tree are from this working group. However, the Decision Tree is widely applicable in other areas of metrology, as illustrated in examples of application to measurements of radionuclides and of the efficiency of a thermistor power sensor. The Decision Tree is intended for use after choices will have been made about the measurement results that qualify for inclusion in the calculation of the key comparison reference value (KCRV), and about the measurement results for which degrees of equivalence should be produced. Both these choices should be based on substantive considerations, not on purely statistical criteria. However, the Decision Tree does not require that the measurement results selected for either purpose be mutually consistent. The Decision Tree should be used as a guide, not as the sole and autonomous determinant of the model that should be selected for the measurement results obtained in a KC, or of the procedure that should be employed to reduce these results. The scientists running the KCs ultimately have the freedom and responsibility to make the corresponding choices that they deem most appropriate and that best fit the purpose of each KC. The Decision Tree involves three statistical tests, and comprises five terminal leaves, which correspond to as many alternative ways in which the KCRV, its associated uncertainty, and the degrees of equivalence (DoEs) may be computed. This contribution does not purport to suggest that any of the KCRVs, associated uncertainties, or DoEs, presented in previously approved final reports issued by working groups of the CCs should be modified. Neither do the alternative results question existing, demonstrated calibration and measurement capabilities (CMCs), nor do they support any new CMCs. [ABSTRACT FROM AUTHOR]

A particular concerns of researchers in statistical inference is bias in parameters estimation. Maximum likelihood estimators are often biased and for small sample size, the first order bias of them can be large and so it may influence the efficiency of the estimator. There are different methods for reduction of this bias. In this paper, we proposed a modified maximum likelihood estimator for the shape parameter of two popular skew distributions, namely skew-normal and skew-t, by offering a new method. We show that this estimator has lower asymptotic bias than the maximum likelihood estimator and is more efficient than those based on the existing methods. [ABSTRACT FROM AUTHOR]

This is the rejoinder of the discussion article: env‐19‐0145, DOI: 10.1002/env.2628 [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Epidemiological studies on periodontal disease (PD) collect relevant bio-markers, such as the clinical attachment level (CAL) and the probed pocket depth (PPD), at pre-specified tooth sites clustered within a subject's mouth, along with various other demographic and biological risk factors. Routine cross-sectional evaluation are conducted under a linear mixed model (LMM) framework with underlying normality assumptions on the random terms. However, a careful investigation reveals considerable non-normality manifested in those random terms, in the form of skewness and tail behavior. In addition, PD progression is hypothesized to be spatially-referenced, i.e. disease status at proximal tooth-sites may be different from distally located sites, and tooth missingness is non-random (or informative), given that the number and location of missing teeth informs about the periodontal health in that region. To mitigate these complexities, we consider a matrix-variate skew-$t$ formulation of the LMM with a Markov graphical embedding to handle the site-level spatial associations of the bivariate (PPD and CAL) responses. Within the same framework, the non-randomly missing responses are imputed via a latent probit regression of the missingness indicator over the responses. Our hierarchical Bayesian framework powered by relevant Markov chain Monte Carlo steps addresses the aforementioned complexities within an unified paradigm, and estimates model parameters with seamless sharing of information across various stages of the hierarchy. Using both synthetic and real clinical data assessing PD status, we demonstrate a significantly improved fit of our proposition over various other alternative models. [ABSTRACT FROM AUTHOR]

This paper proposes dynamic treatment regimes (DTRs) as effective individualized treatment strategies for managing chronic periodontitis. The proposed DTRs are studied via SMARTp—a two‐stage sequential multiple assignment randomized trial (SMART) design. For this design, we propose a statistical analysis plan and a novel cluster‐level sample size calculation method that factors in typical features of periodontal responses such as non‐Gaussianity, spatial clustering, and nonrandom missingness. Here, each patient is viewed as a cluster, and a tooth within a patient's mouth is viewed as an individual unit inside the cluster, with the tooth‐level covariance structure described by a conditionally autoregressive structure. To accommodate possible skewness and tail behavior, the tooth‐level clinical attachment level (CAL) response is assumed to be skew‐t, with the nonrandomly missing structure captured via a shared parameter model corresponding to the missingness indicator. The proposed method considers mean comparison for the regimes with or without sharing an initial treatment, where the expected values and corresponding variances or covariance for the sample means of a pair of DTRs are derived by the inverse probability weighting and method of moments. Simulation studies are conducted to investigate the finite‐sample performance of the proposed sample size formulas under a variety of outcome‐generating scenarios. An R package SMARTp implementing our sample size formula is available at the Comprehensive R Archive Network for free download. [ABSTRACT FROM AUTHOR]

We introduce a new family of multivariate distributions by taking the component-wise Tukey- h transformation of a random vector following a skew-normal distribution with an alternative parameterization. The proposed distribution is named the skew-normal-Tukey- h distribution and is an extension of the skew-normal distribution for handling heavy-tailed data. We compare this proposed distribution to the skew- t distribution, which is another extension of the skew-normal distribution for modeling tail-thickness, and demonstrate that when there are substantial differences in marginal kurtosis, the proposed distribution is more appropriate. Moreover, we derive many appealing stochastic properties of the proposed distribution and provide a methodology for the estimation of the parameters that can be applied to large dimensions. Using simulations, as well as a wine and a wind speed data application, we illustrate how to draw inferences based on the multivariate skew-normal-Tukey- h distribution. [ABSTRACT FROM AUTHOR]

Shannon and Rényi entropies are two important measures of uncertainty for data analysis. These entropies have been studied for multivariate Student-t and skew-normal distributions. In this paper, we extend the Rényi entropy to multivariate skew-t and finite mixture of multivariate skew-t (FMST) distributions. This class of flexible distributions allows handling asymmetry and tail weight behavior simultaneously. We find upper and lower bounds of Rényi entropy for these families. Numerical simulations illustrate the results for several scenarios: symmetry/asymmetry and light/heavy-tails. Finally, we present applications of our findings to a swordfish length-weight dataset to illustrate the behavior of entropies of the FMST distribution. Comparisons with the counterparts—the finite mixture of multivariate skew-normal and normal distributions—are also presented.

The accurate prediction of wildfire behavior and spread is possible only when fire and atmosphere simulations are coupled. In this work, we present a mechanism that causes a small fire to intensify by altering the atmosphere. These alterations are caused by fire-related fluxes at the surface. The fire plume and fluxes increase the convective available potential energy (CAPE) and the chance of the development of a strong pyroconvection system. To study this possible mechanism, we used WRF-Fire to capture fire line propagation as the result of interactions between heat and moisture fluxes, pressure perturbations, wind shear development and dry air downdraft. The wind patterns and dynamics of the pyroconvection system are simulated for the Horse River wildfire at Fort McMurray, Canada. The results revealed that the updraft speed reached up to 12 m/s. The entrainment mixed the mid and upper-level dry air and lowered the atmospheric moisture. The mid-level and upper-level dew point temperature changed by 5–10 ∘ C in a short period of time. The buoyant air strengthened the ascent as soon as the nocturnal inversion was eliminated by daytime heating. The 887 J/kg total increase of CAPE in less than 5 h and the high bulk Richardson number (BRN) of 93 were indicators of the growing pyro-cumulus cell. The presented simulation has not improved the original model or supported leading-edge numerical weather prediction (NWP) achievements, except for adapting WRF-Fire for Canadian biomass fuel. However, we were able to present a great deal of improvements in wildfire nowcasting and short-term forecasting to save lives and costs associated with wildfires. The simulation is sufficiently fast and efficient to be considered for a real-time operational model. While the project was designed and succeeded as an NWP application, we are still searching for a solution for the intractable problems associated with political borders and the current liable authorities for the further development of a new generation of national atmosphere–wildfire forecasting systems.

Several measures of multivariate skewness for scale mixtures of skew-normal distributions are derived. As a special case, those of multivariate skew-t distribution are considered in detail. Furthermore, the similarities, differences, and behavior of these measures are explored for cases of some specific members of the multivariate skew-normal and skew-t distributions using a simulation study. Since some measures are vectors, it is better to take all measures in the same scale when comparing them. In order to attain such a set of comparable indices, the sample version is considered for each of the skewness measures that are taken as test statistics for the hypothesis of t distribution against skew-t distribution. An application is reported for the data set consisting of 71 total glycerol and magnesium contents in Grignolino wine. [ABSTRACT FROM AUTHOR]

In the recent years, the notion of data depth has been used in nonparametric multivariate data analysis since it gives natural ‘centre-outward’ ordering of multivariate data points with respect to the given data cloud. In the literature, various nonparametric tests are developed for testing equality of location of two multivariate distributions based on data depth. Here, we define two nonparametric tests based on two different test statistic for testing equality of locations of two multivariate distributions. In the present work, we compare the performance of these tests with the tests developed by Li and Liu [New nonparametric tests of multivariate locations and scales using data depth. Statist Sci. 2004;(1):686–696] for testing equality of locations of two multivariate distributions. Comparison in terms of power is done for multivariate symmetric and skewed distributions using simulation for three popular depth functions. Application of tests to real life data is provided. Conclusion and recommendations are also provided. [ABSTRACT FROM AUTHOR]

We obtain the first four moments of scale mixtures of skew-normal distributions allowing for scale parameters. The first two moments of their quadratic forms are obtained using those moments. Previous studies derived the moments, but all relevant results do not allow for scale parameters. In particular, it is shown that the mean squared error becomes an unbiased estimator of σ2with skewed and heavy-tailed errors. Two measures of multivariate skewness are calculated. [ABSTRACT FROM PUBLISHER]

Characteristic functions play an important role in probability and statistics; however, a rigorous derivation of these functions requires contour integration, which is unfamiliar to most statistics students. Without resorting to contour integration, Datta and Ghosh (2007) derived the characteristic functions of normal, Cauchy, and double exponential distributions. Here, we derive the characteristic functions of t, truncated normal, skew-normal, and skew-t distributions. The characteristic functions of normal, cauchy distributions are obtained as a byproduct. The derivations are straightforward and can be presented in statistics masters theory classes. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

. 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. [ABSTRACT FROM AUTHOR]

. We study the Jeffreys prior and its properties for the shape parameter of univariate skew- t distributions with linear and nonlinear Student's t skewing functions. In both cases, we show that the resulting priors for the shape parameter are symmetric around zero and proper. Moreover, we propose a Student's t approximation of the Jeffreys prior that makes an objective Bayesian analysis easy to perform. We carry out a Monte Carlo simulation study that demonstrates an overall better behaviour of the maximum a posteriori estimator compared with the maximum likelihood estimator. We also compare the frequentist coverage of the credible intervals based on the Jeffreys prior and its approximation and show that they are similar. We further discuss location-scale models under scale mixtures of skew-normal distributions and show some conditions for the existence of the posterior distribution and its moments. Finally, we present three numerical examples to illustrate the implications of our results on inference for skew- t distributions. [ABSTRACT FROM AUTHOR]

The multivariate skew-normal distribution and the elliptically contoured distributions have been developed to model a sample of independent and identically distributed ran- dom vectors. Recently, various proposals have been made to extend those distributions to the setting of spatial random fields. We describe identifiability problems associated with inference for those proposals and suggest simple remedies. We also describe some properties of the resulting spatial random fields. [ABSTRACT FROM AUTHOR]

Sample selection arises often in practice as a result of the partial observability of the outcome of interest in a study. In the presence of sample selection, the observed data do not represent a random sample from the population, even after controlling for explanatory variables. That is, data are missing not at random. Thus, standard analysis using only complete cases will lead to biased results. Heckman introduced a sample selection model to analyze such data and proposed a full maximum likelihood estimation method under the assumption of normality. The method was criticized in the literature because of its sensitivity to the normality assumption. In practice, data, such as income or expenditure data, often violate the normality assumption because of heavier tails. We first establish a new link between sample selection models and recently studied families of extended skew-elliptical distributions. Then, this allows us to introduce a selection-t (SLt) model, which models the error distribution using a Student's t distribution. We study its properties and investigate the finite-sample performance of the maximum likelihood estimators for this model. We compare the performance of the SLt model to the conventional Heckman selection-normal (SLN) model and apply it to analyze ambulatory expenditures. Unlike the SLN model, our analysis using the SLt model provides statistical evidence for the existence of sample selection bias in these data. We also investigate the performance of the test for sample selection bias based on the SLt model and compare it with the performances of several tests used with the SLN model. Our findings indicate that the latter tests can be misleading in the presence of heavy-tailed data. [ABSTRACT FROM AUTHOR]

The skew-normal is a parametric model that extends the normal family by the addition of a shape parameter to account for skewness. As well, the skew-t distribution is generated by a perturbation of symmetry of the basic Student's t density. These families share some nice properties. In particular, they allow a continuous variation through different degrees of asymmetry and, in the case of the skew-t, tail thickness, but still retain relevant features of the perturbed symmetric densities. In both models, a problem occurs in the estimation of the skewness parameter: for small and moderate sample sizes, the maximum likelihood method gives rise to an infinite estimate with positive probability, even when the sample skewness is not too large. To get around this phenomenon, we consider the minimum Hellinger distance estimation technique as an alternative to maximum likelihood. The method always leads to a finite estimate of the shape parameter. Furthermore, the procedure is asymptotically efficient under the assumed model and allows for testing hypothesis and setting confidence regions in a standard fashion. [ABSTRACT FROM AUTHOR]

This paper examines the economic accomplishments of individual members in a Performing Rights Organization (PRO), sometimes referred to as a Performing Rights Society. Today, there is the growing importance of intellectual property and copyright protection for authors and creators of literary, dramatic, musical, artistic and other intellectual works. The digital age has placed added pressure on songwriters, lyricists and composers in their ability to derive economic benefits from their intellectual creativity in the form of a copyright. Copyright laws protect and enable the creation of music by allowing authors and composers to license the control and use of their creations, and receive compensation in the form of royalty payments for their work. The PROs license, collect and distribute royalty payments for non-dramatic public performances of copyrighted musical works created and owned by its members or affiliates. In this paper, skewness and heavy tail of returns in the form of member royalty payments are estimated using the skew-normal and skew- t distributions in a parametric approach. We found strong evidence of the so-called ‘superstar effect’ in which the average royalty payment made by a PRO is still dominated by extreme outcomes, and relatively few members earned a substantial share of royalty payments from blockbuster hits that have endured over time. There is little evidence of smaller niche members dominating or replacing the ‘superstars.’ Economists and others will benefit from this empirical study which emphasizes a new understanding of the music industry from a PRO, member royalty payment and performance copyright perspective. [ABSTRACT FROM AUTHOR]

Abstract: Linear mixed models based on the normality assumption are widely used in health related studies. Although the normality assumption leads to simple, mathematically tractable, and powerful tests, violation of the assumption may easily invalidate the statistical inference. Transformation of variables is sometimes used to make normality approximately true. In this paper we consider another approach by replacing the normal distributions in linear mixed models by skew-t distributions, which account for skewness and heavy tails for both the random effects and the errors. The full likelihood-based estimator is often difficult to use, but a 3-step estimation procedure is proposed, followed by an application to the analysis of deglutition apnea duration in normal swallows. The example shows that skew-t models often entail more reliable inference than Gaussian models for the skewed data. [Copyright &y& Elsevier]

We derive the extreme value distribution of the skew-symmetric family, the probability density function of the latter being defined as twice the product of a symmetric density and a skewing function. We show that, under certain conditions on the skewing function, this extreme value distribution is the same as that for the symmetric density. We illustrate our results using various examples of skew-symmetric distributions as well as two data sets. [ABSTRACT FROM AUTHOR]

The assumption of symmetry is often incorrect in real-life statistical modeling due to asymmetric behavior in the data. This implies a departure from the well-known assumption of normality defined for innovations in time series processes. In this paper, the autoregressive (AR) process of order p (i.e., the AR(p) process) is of particular interest using the skew generalized normal (SGN) distribution for the innovations, referred to hereafter as the ARSGN( p ) process, to accommodate asymmetric behavior. This behavior presents itself by investigating some properties of the SGN distribution, which is a fundamental element for AR modeling of real data that exhibits non-normal behavior. Simulation studies illustrate the asymmetry and statistical properties of the conditional maximum likelihood (ML) parameters for the ARSGN( p ) model. It is concluded that the ARSGN( p ) model accounts well for time series processes exhibiting asymmetry, kurtosis, and heavy tails. Real time series datasets are analyzed, and the results of the ARSGN( p ) model are compared to previously proposed models. The findings here state the effectiveness and viability of relaxing the normal assumption and the value added for considering the candidacy of the SGN for AR time series processes. [ABSTRACT FROM AUTHOR]