The research assesses the breadth of the definition of "distributions" and asks whether this definition may be too broad. Is regulation found wanting because the definition results in improper protection of the interests of creditors, even with the modern approach of applying the solvency and liquidity test? In answering this question, the South African position is assessed and the position in New Zealand researched for comparative purposes. / Dissertation (LLM (Corporate Law))--University of Pretoria, 2021. / Mercantile Law / LLM (Corporate Law) / Unrestricted

In this thesis, we investigate the estimation problem of treatment effect from Bayesian perspective through which one can first obtain the posterior distribution of unobserved potential outcome from observed data, and then obtain the posterior distribution of treatment effect. We mainly consider how to represent a joint distribution of two potential outcomes - one from treated group and another from control group, which can give us an indirect impression of correlation, since the estimation of treatment effect depends on correlation between two potential outcomes. The first part of this thesis illustrates the effectiveness of adapting Gaussian mixture models in solving the treatment effect problem. We apply the mixture models - Gaussian Mixture Regression (GMR) and Gaussian Mixture Linear Regression (GMLR)- as a potentially simple and powerful tool to investigate the joint distribution of two potential outcomes. For GMR, we consider a joint distribution of the covariate and two potential outcomes. For GMLR, we consider a joint distribution of two potential outcomes, which linearly depend on covariate. Through developing an EM algorithm for GMLR, we find that GMR and GMLR are effective in estimating means and variances, but they are not effective in capturing correlation between two potential outcomes. In the second part of this thesis, GMLR is modified to capture unobserved covariance structure (correlation between outcomes) that can be explained by latent variables introduced through making an important model assumption. We propose a much more efficient Pre-Post EM Algorithm to implement our proposed GMLR model with unobserved covariance structure in practice. Simulation studies show that Pre-Post EM Algorithm performs well not only in estimating means and variances, but also in estimating covariance.

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In recent years, the need for models which can accommodate higher order covariates have increased greatly. We first consider linear regression with vector-valued response Y and tensor-valued predictors X. Envelope models (Cook et al., 2010) can significantly improve the estimation efficiency of the regression coefficients by linking the regression mean with the covariance of the regression error. Most existing tensor regression models assume that the conditional distribution of Y given X follows a normal distribution, which may be violated in practice. In Chapter 2, we propose an envelope multivariate linear regression model with tensor-valued predictors and elliptically contoured error distributions. The proposed estimator is more robust to violations of the error normality assumption, and it is more efficient than the estimators without considering the underlying envelope structure. We compare the new proposal with existing estimators in extensive simulation studies. In Chapter 3, we explore how the missing data problem can be addressed for multivariate linear regression setting with envelopes and elliptical error. A popular and efficient approach, multiple imputation is implemented with bootstrapped expectation-maximization (EM) algorithm to fill the missing data, which is then followed with an adjustment in estimating regression coefficients. Simulations with synthetic data as well as real data are presented to establish the superiority of the adjusted multiple imputation method proposed. / Statistics

Information regarding spatiotemporal trends in young-of-year (YOY) fish distributions gives managers insight into recruitment and ultimately adult population variability. In Puerto Rico, limited research has been conducted on YOY distributions with no studies addressing reservoir systems. A comparison of the efficacy of two sampling gears and an assessment of spatiotemporal distributions of YOY fish communities in a tropical reservoir were conducted. Diversity of catch between push nets and offshore light traps were similar, though species composition of catch was different between gears. Inshore light traps collected greater total numbers and diversities of the YOY fish community than offshore traps in spring and summer seasons. Catch per unit effort was greater in the spring for inshore traps whereas CPUE was greater in offshore traps in the fall. These results will allow managers to coordinate YOY fish sampling efforts for specific species with periods of peak abundance and preferred habitat.

Understanding the impact of late season precipitation on the distribution of cotton yields provides insight into managing yield risks. This research combines Linear Moment Models with historical weather data to assess the impact of late season precipitation extremes on cotton production and revenue. The empirical analysis suggests that late season drought reduces both mean yield and variance. The shift in variance is coupled with an exchange of upside risk for downside risk implying that the variance reduction alone masks an important effect on producer’s risk. Revenue impacts suggest high revenue for irrigated acreage as compared to dryland acreage, and the late season drought impact on revenue shows that the use of irrigation causes increases in revenue as compared to dryland acreage.

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<p> The (t,p) reaction has been performed on targets of 151Sm, 176Yb and 178Hf. The experiment was performed with 15 MeV tritons. The outgoing protons were analyzed with the Enge split-pole spectrograph. Angular distributions were measured for all three nuclei with special emphasis being placed on L=0 transitions.</p> <p> The angular distributions for the 151Sm(t,p)153Sm reaction showed that the distribution of L=0 strength among the low-lying states is not consistent with expectations based on the detailed wavefunctions for 151Sm and 153Sm calculated by two independent groups; Katajanheimo and Hammaren (1978) and Rekstad et al. (1978). The distributions also showed that the total L=0 strength, summed over the four observed states in 153Sm, is much less than for neighbouring nuclei.</p> <p> Angular distributions of the (t,p) reaction on 176Yb and 178Hf targets showed strong L=0 transitions to levels at ~ 1.3 MeV excitation. It is believed that the N=108 energy gap in the Nilsson diagram is the cause of the large L=0 strength observed. At present no quanitative calculation has reproduced the observed phenomenon, however a calculation based on the Volkov model is presently being considered.</p> / Thesis / Master of Science (MSc)

<p> Several test statistics, which are known, can be used for testing for exponentiality. A new test statistic TE is proposed. TE is based on a censored sample and is similar to Tiku's T statistic for testing for normality. The distribution of TE tends to normality with increasing sample size. Besides, TE is easy to compute and is both origin and scale invariant. The power of TE for non-exponential distributions is comparable with Shapiro & Wilk statistic W-exponential. </p> / Thesis / Master of Science (MSc)

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