Small scale distributions of Mellita tenuis and Encope spp. were quantified at Fort De Soto Park on Mullet Key, off Egmont Key and off Captiva Island, Florida during 2005. Off Captiva Island, Encope spp. were aggregated in 33.3% of plots in March. Off Egmont Key, M. tenuis were aggregated in 100% of plots in March but in no plots in September. At Fort De Soto Park, M. tenuis were aggregated in 37.5% of plots in May 12.5% in July and 50.0% in September. Sand dollars in 6.3% of the plots in September at Fort De Soto had a uniform distribution. Individuals in all other plots at all sites had random distributions. At Fort De Soto, each plot was revisited a few hours after the initial observation; 37.5% of plots had a different distribution at the second observation. Percent organic content of the smallest sediment grains (<105 μm) was not correlated with sand dollar distribution, except off Egmont Key. There was a significant negative correlation between nearest neighbor index and percent organic content. Mellita tenuis do aggregate on occasion. The cause of aggregation is not known. If localized differences in percent organic content of the sediment influence distribution, then homogeneity in the percent organic content of the sediment, as found in the majority of plots, would suggest random distribution of sand dollars.

This dissertation is composed of three articles describing novel approaches for analysis and modeling using multivariate skew-normal and skew-t distributions in econometrics and environmetrics. In the first article we introduce the Heckman selection-t model. Sample selection arises often 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. 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. This then allows us to introduce a selection-t 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 selection-t model to the Heckman selection model and apply it to analyze ambulatory expenditures. In the second article we introduce a family of multivariate log-skew-elliptical distributions, extending the list of multivariate distributions with positive support. We investigate their probabilistic properties such as stochastic representations, marginal and conditional distributions, and existence of moments, as well as inferential properties. We demonstrate, for example, that as for the log-t distribution, the positive moments of the log-skew-t distribution do not exist. Our emphasis is on two special cases, the log-skew-normal and log-skew-t distributions, which we use to analyze U.S. precipitation data. Many commonly used statistical methods assume that data are normally distributed. This assumption is often violated in practice which prompted the development of more flexible distributions. In the third article we describe two such multivariate distributions, the skew-normal and the skew-t, and present commands for fitting univariate and multivariate skew-normal and skew-t regressions in the statistical software package Stata.

Sport and dance injuries have increased despite improvements in coaching techniques and medical care. Other factors, including psychological ones, were therefore thought to play a role in injury vulnerability. Most of the attempts to explain how psychological variables can affect an athlete's predisposition to injury have been based on anxiety or stress concepts. In this survey type study an interactive approach to stress has been adopted with the goal of finding a relationship between stress and injury in a group of professional ballet dancers. No simple direct relationship was found. Multiple regression analysis was performed and a more complicated relationship between stress indicators and injury was found. When an attempt was made to investigate the significant interaction, no significant correlations were found. However, the correlations were found to be large and negative. This could indicate that if the sample size had been larger significant correlations may have been found. / Psychology / M.A. (Psychology)

Sport and dance injuries have increased despite improvements in coaching techniques and medical care. Other factors, including psychological ones, were therefore thought to play a role in injury vulnerability. Most of the attempts to explain how psychological variables can affect an athlete's predisposition to injury have been based on anxiety or stress concepts. In this survey type study an interactive approach to stress has been adopted with the goal of finding a relationship between stress and injury in a group of professional ballet dancers. No simple direct relationship was found. Multiple regression analysis was performed and a more complicated relationship between stress indicators and injury was found. When an attempt was made to investigate the significant interaction, no significant correlations were found. However, the correlations were found to be large and negative. This could indicate that if the sample size had been larger significant correlations may have been found. / Psychology / M.A. (Psychology)