Thesis (MComm)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: In this study Portfolio Opportunity Distributions (PODs) is applied as an alternative performance evaluation method. Traditionally, Broad-Market Indices or peer group comparisons are used to perform performance evaluation. These methods however have various biases and other problems related to its use. These biases and problems include composition bias, classification bias, concentration, etc. R.J. Surz (1994) introduced PODs in order to eliminate some of these problems. Each fund has its own opportunity set based on its style mandate and constraints. The style mandate of the fund is determined by calculating the fund’s exposure to the nine Surz Style Indices through the use of Returns-Based Style Analysis (RBSA). The indices are created based on the style proposed by R.J. Surz (1994). Some adjustments were made to incorporate the unique nature of the South African equity market. The combination of the fund’s exposures to the indices best explains the return that the fund generated. In this paper the fund’s constraints are based on the regulation requirements imposed on the funds in South Africa by the Collective Investment Schemes Control Act No. 45 of 2002 (CISCA). Thousands of random portfolios are then generated based on the fund’s opportunity set. The return and risk of the simulated portfolios represent the possible investment outcomes that the manager could have achieved given its opportunity set. Together the return and risk of the simulated portfolios represent a range of possible outcomes against which the performance of the fund is compared. It is also possible to determine the skill of the manager since it can be concluded that a manager who consistently outperforms most of the simulated portfolios shows skill in selecting shares to be included in the portfolio and assigning the correct weights to these shares. The South African Rand depreciated quite a bit during the period under evaluation and therefore funds invested large portions of their assets in foreign investments. These investments mostly yielded very high or very low returns compared to the returns available in the domestic equity market which impacted the application of PODs. Although the PODs methodology shows great potential, it is impossible to conclude with certainty whether the PODs methodology is superior to the traditional methods based on the current data. / AFRIKAANSE OPSOMMING: In hierdie studie word Portefeulje Geleentheids Verdelings (“PODs”) bekendgestel as ‘n alternatiewe manier om die obrengste van bestuurders te evalueer. Gewoonlik word indekse en die vergelyking van die fonds met soortgelyke fondse gebruik om fondse te evalueer. Die metodes het egter verskeie probleme wat met die gebruik daarvan verband hou. Die probleme sluit onder andere in: die samestelling en klassifikasie van soortgelyke fondse, die konsentrasie in die mark, ens. R.J. Surz (1994) het dus Portefeulje Geleentheids Verdelings (“PODs”) bekendgestel in ‘n poging om sommige van die probeleme te elimineer. Elke fonds het sy eie unieke geleentheids versameling wat gebaseer is op die fonds se styl en enige beperkings wat op die fonds van toepassing is. Die fonds se styl word bepaal deur die fonds se blootstelling aan die nege Surz Styl Indekse te meet met behulp van opbrengs-gebaseerde styl analise (“RBSA”). Die indekse is geskep gebaseer op die metode wat deur R.J. Surz (1994) voorgestel is. Daar is egter aanpassings gemaak om die unieke aard van die Suid-Afrikaanse aandele mark in ag te neem. Die kombinasie van die fonds se blootstelling aan die indekse verduidelik waar die fonds se opbrengs vandaan kom. In die navorsingstuk is die beperkings wat van toepassing is op die fonds afkomstig uit die regulasie vereistes wat deur die “Collective Investment Schemes Control Act No. 45 of 2002 (CISCA)” in Suid-Afrika op fondse van toepassing is. Duisende ewekansige portefeuljes word dan gegenereer gebaseer op die fonds se unieke groep aandele waarin die fonds kan belê. Die opbrengs en risiko van die gesimuleerde portefeuljes verteenwoordig al die moontlike beleggings uitkomste wat die fonds bestuurder kon gegenereer het gegewe die fonds se unieke groep aandele waarin dit kon belê. Die opbrengs en risiko van al die gesimuleerde portefeuljes skep saam ‘n verdeling van moontlike beleggings uitkomste waarteen die opbrengs en risiko van die fonds vergelyk word. Hierdie proses maak dit moontlik om die fonds bestuurder se vermoë om beter as meeste van die gesimuleerde portefeuljes te presteer te bepaal. Die aanname kan gemaak word dat ‘n bestuurder wat konsekwent oor tyd beter as meeste van die gesimuleerde portefeuljes presteer oor die vermoë beskik om die regte aandele te kies om in die portefeulje in te sluit en ook die regte gewigte aan die aandele toe te ken. Die Suid-Afrikaanse Rand het heelwat gedepresieer tydens die evaluasie periode en daarom het fondse groot porsies van hul beleggings oorsee belê. Die beleggings het dus of heelwat groter of heelwat kleiner opbrengste gehad in vergelyking met die opbrengste beskikbaar in die plaaslike aandelemark en dit het die toepassing van PODs beïnvloed. PODs toon baie potential, maar dit is egter onmoontlik om met die huidige data stel vas te stel of dit ‘n beter metode is.

Thesis (MSc )--Stellenbosch University, 2010. / ENGLISH ABSTRACT: The patterns of spread of non-indigenous species and the factors influencing their distribution have been studied infrequently on Southern Ocean Islands, where the prevention and control of biological invasions is a priority for conservation management. Owing to its remoteness and relatively small size, sub-Antarctic Marion Island provides an ideal opportunity to investigate the patterns of spread of invasive species and the factors likely influencing the distribution of alien species. Therefore, this study provides a spatially explicit documentation of the alien and invasive vascular plant species on Marion Island, the change in their distribution patterns through time, an assessment of the correlates of the current distributions, documentation of species rich areas, and provides recommendations for control based on these data and life history data available for each species. To ensure comprehensive coverage for the current estimate of distributions, a combination of a systematic (spatially explicit) survey and an ad hoc data collection method was used to examine the abundance and occupancy of each alien plant species across the island. The spatially explicit survey was used to identify sampling sites on a ½ minute by ½ minute scale (926 m × 926 m) which resulted in 348 sites across the island, whereas 2356 additional presence records were added during the ad hoc sampling. The residence time of each species was also estimated from the first records reported in various literature. While it has been documented in many studies that residence time is an important factor explaining species distribution, this study showed that distribution of alien species on Marion Island is not explained by residence time. The alien plant species on Marion Island differ markedly in their occupancy, distribution and rate of expansion. Agrostis stolonifera, Cerastium fontanum, Poa annua and Sagina procumbens are all expanding their ranges, whereas the range of Stellaria media appears to be contracting. Cerastium fontanum is the most widespread species on Marion Island while Sagina procumbens is the most abundant (number of records) and most rapidly expanding species on both Marion and Prince Edward Islands. Generalized linear models demonstrated that altitude, distance to human disturbed sites, and nearest neighbour presence are all significant and often strong correlates of spatial variation in alien vascular plant species richness and individual species presences on Marion Island. In particular, alien species richness on Marion Island declines sharply with increasing elevation, and that the distribution of the most widespread species is spatially aggregated. The surroundings of the Meteorological station and Mixed Pickle hut exhibit high richness and a high likelihood of the presence of individual species. None of the models developed for this study resulted in habitat type being significant explanatory variable for the distribution of any of the alien plant species, although from the records alone it is clear that the salt spray vegetation type is avoided. Together with assessments of the life history of the species, the current distribution data suggest that few alien plant species can be easily eradicated. Most are already too widespread already for cost effective eradication. Moreover, given the current rate of spread of Agrostis stolonifera, Cerastium fontanum, Poa annua and Sagina procumbens, and their apparent lack of habitat preference, it seems likely that within the next few decades many lowland habitats will be dominated by these species. By contrast, Rumex acestosella, Agrostis gigantea, Agropyron repens, Juncus effusus, Luzula cf. multiflora and the newly established shrub species should be the subject of control or eradication efforts. This thesis provides comprehensive baseline data on alien vascular plant distributions as a benchmark for future assessments. / AFRIKAANSE OPSOMMING: Die verspreidingspatrone van uitheemse spesies en die faktore wat hulle verspreiding beïnvloed is selde op Suidelike Oseaan Eilande bestudeer, waar die voorkoming en beheer van biologiese indringing ‘n prioriteit is vir bewaringsbestuur. Te danke aan sy afgeleëndheid en relatiewe klein grootte, voorsien sub-Antarktiese Marion Eiland ‘n ideale geleentheid om die patrone van verspreiding van indringer spesies en die faktore wat moontlik die verspreiding van uitheemse spesies beïnvloed te ondersoek. Daarom voorsien hierdie studie ‘n ruimtelik eksplisiete dokumentering van die uitheemse en indringer vaatplant spesies op Marion Eiland, die verandering in hulle verspreidingspatrone oor tyd, ‘n bepaling van die korrelasies van die huidige verspreidings, dokumentering van spesiesryke areas, en voorsien aanbevelings vir beheer gebasseer op hierdie data en die lewensloopdata beskikbaar vir elke spesie. Om omvattende dekking vir die huidige skatting van vespreidings te verseker, is ‘n kombinasie van sistematiese en ad hoc metodes gebruik om die talrykheid en besetting van elke uitheemse spesie oor die eiland te ondersoek. Die ruimtelik eksplisiete opname is gebruik om moniteringsplotte op ‘n ½ minuut by ½ minuut skaal (926 m × 926 m), met die resultaat van 348 plotte oor die eiland, terwyl 2356 addisionele voorkomsrekords bygevoeg is tydens die ad hoc versameling. Die verblyftyd van elke spesie is ook beraam vanaf die eerste rekords in die literatuur. Terwyl dit aangeteken is dat verblyftyd ‘n belangrike faktor is om spesie verspreiding te verduidelik, wys hierdie studie dat verspreiding van uitheemse spesies op Marion Eiland nie verduidelik word deur verblyftyd nie. Die uitheemse spesies op Marion Eiland verskil aansienlik in hulle besetting, verspreiding en tempo van uitbreiding. Agrostis stolonifera, Cerastium fontanum, Poa annua en Sagina procumbens brei almal hulle areas uit, terwyl die area van Stellaria media bleik te krimp. Cerastium fontanum is die mees wydverspreide spesie op Marion Eiland, terwyl Sagina procumbens die oorvloedigste (aantal rekords) en die vinnigste uitbreidende spesie is op beide Marion en Prince Edward Eiland. Veralgemeende lineêre modelle het aangetoon dat hoogte, afstand na menslike versteurde plotte, en naaste buurman teenwoordigheid almal betekenisvol is en gereeld sterk korreleer met ruimtelike variasie in uitheemse vaatplant spesierykheid en individuele spesie voorkoms op Marion Eiland. Uitheemse spesierykheid op Marion Eiland neem in besonder sterk af met ‘n toename in hoogte en die verspreiding van die mees wyduitgebreide spesies is ruimtelik saamgesteld. Die omgewing om die Weerstasie en Mixed Pickle hut toon hoë rykheid en ‘n hoë waarskynlikheid van die voorkoms van individuele spesies. Nie een van die modelle wat vir hierdie studie ontwikkel is toon ‘n belangrikheid in habitat tipe as ‘n verduidelikbare veranderlike vir die verspreiding van enige van die uitheemse plant spesies nie, alhoewel vanuit die rekords alleen is dit duidelik dat soutsproei plantegroei nie verkies word nie. Tesame met ondersoeke oor die lewensloop van die spesies, stel die huidige verspreidingsdata voor dat min uitheemse plant spesies maklik uitgeroei kan word. Die meeste is eenvoudig te wydverspreid vir koste effektiewe uitroeiing. Voorts, gegewe die huidige tempo van uitbreiding van Agrostis stolonifera, Cerastium fontanum, Poa annua en Sagina procumbens en hulle skynbare gebrek aan habitat voorkeur, is dit hoogs waarskynlik dat baie van die laerliggende habitatte binne die volgende paar dekades gedomineer sal word deur hierdie spesies. In teenstelling, Rumex acestosella, Agrostis gigantea, Agropyron repens, Juncus effusus, Luzula cf. multiflora en die nuutgevestigde struik spesie moet die fokus wees van beheer/uitroeiing pogings. Hierdie tesis voorsien omvattende basislyn data oor uitheemse vaatplantverspreidings as ‘n standaard vir toekomstige ondersoeke. / This project was funded by the South African National Antarctic Programme of the National Research Foundation (NRF – SANAP). Additional funding was provided by The Prince Edward Islands book fund.

In this study, we consider the generalized function solutions to nonlinear wave equation with distribution initial data. J. F. Colombeau shows that the initial value problem u_tt - Δu = F(u); m(x,0) = U_0; u_t (x,0) = i_1 where the initial data u_0 and u_1 are generalized functions, has a unique generalized function solution u. Here we take a specific F and specific distributions u_0, u_1 then inspect the generalized function representatives for the initial value problem solution to see if the generalized function solution is a distribution or is more singular. Using the numerical technics, we show for specific F and specific distribution initial data u_0, u_1, there is no distribution solution.

Doctor of Philosophy / Department of Statistics / Gary L. Gadbury / High-throughput metabolite analysis is an approach used by biologists seeking to identify the functions of genes. A mutation in a gene encoding an enzyme is expected to alter the level of the metabolites which serve as the enzyme’s reactant(s) (also known as substrate) and product(s). To find the function of a mutated gene, metabolite data from a wild-type organism and a mutant are compared and candidate reactants and products are identified. The screening principle is that the concentration of reactants will be higher and the concentration of products will be lower in the mutant than in wild type. This is because the mutation reduces the reaction between the reactant and the product in the mutant organism. Based upon this principle, we suggest a method to screen the possible lipid reactant and product pairs related to a mutation affecting an unknown reaction. Some numerical facts are given for the treatment means for the lipid pairs in each treatment group, and relations between the means are found for the paired lipids. A set of statistics from the relations between the means of the lipid pairs is derived. Reactant and product lipid pairs associated with specific mutations are used to assess the results. We have explored four methods using the test statistics to obtain a list of potential reactant-product pairs affected by the mutation. The first method uses the parametric bootstrap to obtain an empirical null distribution of the test statistic and a technique to identify a family of distributions and corresponding parameter estimates for modeling the null distribution. The second method uses a mixture of normal distributions to model the empirical bootstrap null. The third method uses a normal mixture model with multiple components to model the entire distribution of test statistics from all pairs of lipids. The argument is made that, for some cases, one of the model components is that for lipid pairs affected by the mutation while the other components model the null distribution. The fourth method uses a two-way ANOVA model with an interaction term to find the relations between the mean concentrations and the role of a lipid as a reactant or product in a specific lipid pair. The goal of all methods is to identify a list of findings by false discovery techniques. Finally a simulation technique is proposed to evaluate properties of statistical methods for identifying candidate reactant-product pairs.

Neutron-induced fission has been studied at different excitation energies of the compound nucleus by measurements on the two fissioning systems, 252Cf* and 239U*. For the first time, the light fission fragment yields from the reaction 251Cf(nth, f) have been measured with high resolution. This experiment was performed with the recoil mass spectrometer LOHENGRIN at ILL in Grenoble, France. When the results from this work, where the compound nucleus is at thermal excitation, are compared to the spontaneous fission of 252Cf, enhanced emission yields as well as an increased mean kinetic energy is observed around A = 115. This suggests the existence of an additional super-deformed fission mode in 252Cf. The reaction 238U(n, f) was studied using the 2E-technique with a double Frisch grid ionization chamber. Fission fragment mass, energy and angular distributions were determined for incident neutron energies between 0.9 and 2.0 MeV. The experiments were performed at the Van de Graaff accelerator of IRMM in Geel, Belgium. This is the first measurement of the mass distribution for incident neutron energies around 0.9 MeV. The motivation for studying 238U(n, f) was to verify theoretical predictions of the mass distribution at the vibrational resonance in the fission cross section at 0.9 MeV. However, the predicted changes in fission fragment distributions could not be confirmed. A precise modelling of the fission process for the minor actinides becomes very important for future generation IV and accelerator driven nuclear reactors. Since fission fragment distributions depend on the excitation of the fissioning system, so does the number of delayed neutrons, which are one of the safety parameters in a reactor.

Climate change and habitat fragmentation are altering the structure and functioning of plant communities world-wide. Understanding how, why and with what consequences are major challenges of ecology today. Trait-based approaches focus on functional rather than taxonomic identity to facilitate process-based explanation and prediction. This thesis develops new ways of operationalising traits to understand plant community responses to the environment and community effects on ecosystem functioning and services. Wetlands, distinct in nature and patchy in their distribution, serve as a natural laboratory to extend plant trait theory and as inspiration for metacommunity modelling. The first part of the thesis (Papers 1 and 2) focuses on wetland plant traits in relation to current and future environmental conditions, ecosystem functioning and ecosystem services. Paper 1 surveys the state of knowledge regarding (i) ultimate and proximate drivers of wetland plant community functional composition, trait covariation and responses of individual traits along gradients, as well as (ii) trait effects on the sets of ecosystem properties and processes that underlie the generation of three key wetland ecosystem services (regulation of water flow, water quality, and climate). Paper 2 modifies species distribution modelling to predict future changes in plant community trait distributions due to climate change in central Sweden, which allows a qualitative estimate of changes in ecosystem service potential. Climate change induced functional changes may benefit water quality and flow regulation provided by fens and riparian wetlands, but compromise carbon sequestration capacity in bogs. The second part of the thesis (Papers 3 and 4) develops trait-based metacommunity models to study the interplay of local and regional dynamics on species, community and whole-metacommunity responses to climate change. Paper 3 finds model assumptions about species dispersal capacity to strongly influence predictions of diversity loss following climate change. While differences in species dispersal capacity drastically increase predicted extinction risk, more realistic models based on an empirically derived seed mass – seed number trade-off strongly moderate these predictions. Without considering fitness effects of covarying traits, models that include variable dispersal capacities thus might overestimate extinction risk from climate change. Paper 4 studies the development and recovery of the regional average trait-lag of response trait distributions, as a direct measure of the instantaneous realised metacommunity response to temperature change with implications for levels of ecosystem functioning. The dynamical response jointly depended on local response capacity and regional adaptive re-organisation via species range shifts. Where habitat was scarce, connectivity network properties mediated response capacity and may guide conservation priorities. This thesis makes contributions to plant trait ecology, wetland functional ecology, ecosystem service science and metacommunity theory. As a whole it furthers progress towards a predictive ecology that can bridge scales from individual physiology to ecosystem dynamics and anticipate global change effects on biodiversity and ecosystem functioning. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 3: Manuscript. Paper 4: Manuscript.</p><p> </p>

Dans cette thèse, on étudie deux thèmes, a priori différents mais qui rentrent dans le cadre des systèmes dynamiques : les échanges d’intervalles, la résolution d’équations cohomologiques et la description explicite des distributions invariantes par certains difféomorphismes d’un groupe de Lie compact.1 - On établit un critère d'existence de fonctions propres continues non constantes pour les échangesd'intervalles, c'est-à-dire de non mélange faible topologique. On construit pour tout entier m > 3des échanges de m intervalles de rang 2 uniquement ergodiques et non topologiquement faiblementmélangeants. Nous répondons aussi à une question de Ferenczi et Zamboni. On construit aussi pourtout entier pair m ≥ 4 des échanges de m intervalles possédant des valeurs propres irrationnelles et desvaleurs propres rationnelles (avec fonctions propres associées continues par morceaux) et qui sont soituniquement ergodiques, soit non minimaux.2 - On montre qu’un échange d’intervalles affine, dont les pentes sont des puissances d’un mêmeentier n, et dont les coupures et leurs images sont des rationnels , a une dynamique très simple : toutesses orbites sont propres et il possède une orbite périodique ou un cycle périodique.3 - On traite deux questions d’analyse sur un groupe de Lie connexe compact G. i) Soient a ∈ Get γ le difféomorphisme de G donné par γ(x) = ax (translation `a gauche par a). On donne lesconditions nécessaires et suffisantes pour que l’équation cohomologique f − f ◦ γ = g admette dessolutions dans l’espace de Fréchet C∞(G) des fonctions complexes C∞ sur G. ii) Lorsque G est le toreTn, on détermine explicitement les distributions sur Tn invariantes par un automorphisme affine γ i.e.γ(x) = Ax + a avec A ∈ GL(n, Z) et a ∈ Tn.4 - On donne des résultats obtenus dans 3) une application aux déformations infinitésimales d’unfeuilletage obtenu par suspension d’une translation d’un groupe de Lie compact. / In this thesis, we study two subjects, which are priori different but are within the scopeof dynamical systems: interval exchange, the resolution of cohomological equationsand the explicit description of invariant distributions by a diffeomorphism on a compactLie group.1. We prove a criterion for the existence of continuous non constant eigenfunc-tions for interval exchange transformations which are non topologically weakly mixing.We first construct, for any m > 3, uniquely ergodic interval exchange transforma-tions of Q-rank 2 with irrational eigenvalues associated to continuous eigenfunctionswhich are not topologically weakly mixing; this answers a question of Ferenczi andZamboni [5]. Moreover we construct, for any even integer m ≥ 4, interval exchangetransformations of Q-rank 2 with both irrational eigenvalues (associated to continuouseigenfunctions) and non trivial rational eigenvalues (associated to piecewise continu-ous eigenfunctions); these examples can be chosen to be either uniquely ergodic ornon minimal.2. We prove that an affine interval exchange, whose slopes are integer powers ofthe same integer n, and whose cuts and their images are rational, has a very simpledynamic: all its orbits are proper and it has a periodic orbit or a periodic cycle.3. A third section deals with two analytic questions on a connected compact Liegroup G. i) Let a ∈ G and denote by γ the diffeomorphism of G given by γ(x) = ax(left translation by a). We give necessary and sufficient conditions for the existenceof solutions of the cohomological equation f − f ◦ γ = g on the Fr´echet space C∞(G)of complex C∞ functions on G. ii) When G is the torus Tn, we compute explicitly thedistributions on Tn invariant by an affine automorphism γ, that is, γ(x) = Ax+a withA ∈ GL(n, Z) and a ∈ Tn.4. We apply the results of the preceding section to describe the infinitesimaldeformations of a foliation obtained by suspension of a translation associated to anelement on a compact Lie group.

O interesse pelos estudos de bioequivalência iniciou-se na década de 60, sendo o FDA (EUA) a primeira agência reguladora a se interessar por esta questão. No Brasil, uma lei de 1999 regulamentou o medicamento genérico no país, sendo este um importante meio de acesso aos medicamentos pela população e fazendo parte da política de medicamentos do SUS. No Brasil, a ANVISA e responsável por inspecionar os centros de bioequivalência bem como dar as diretrizes para estes. Um modelo paramétrico padrão para a etapa estatística e disponibilizado para a decisão de bioequivalência media e espera-se que este ajuste-se aos dados obtidos nos estudos de bioequivalência, o que nem sempre acontece. Neste sentido, e proposto nesta tese o uso de modelos paramétricos mais abrangentes baseados em outras distribuições de probabilidade para a decisão de bioequivalência media e que possam modelar a assimetria dos dados, dispensando o uso da transformação logarítmica para os parâmetros farmacocinéticos o que afeta a amplitude dos limites de bioequivalência. Propõe-se também o uso de modelos bivariados para a tomada conjunta da decisão de bioequivalência media, quando são analisados simultaneamente dois parâmetros farmacocinéticos. Foram utilizados métodos Bayesianos para a estimação dos parâmetros dado a exibilidade deste enfoque quando combinado ao uso dos métodos MCMC facilitados a partir do uso de softwares livres. Nesta tese e apresentado um estudo do poder empírico dos testes de hipóteses para os modelos univariados propostos bem como são introduzidos quatro exemplos, sendo os três primeiros voltados a aplicação da decisão de bioequivalência media e o quarto para a aplicação da bioequivalência populacional e individual. Nos três primeiros exemplos foram observados ganhos em termos de ajuste dos novos modelos propostos aos dados com relação ao modelo padrão segundo os critérios de seleção de modelos utilizados. O exemplo quatro apresenta uma analise padrão de bioequivalência populacional e individual com o código computacional para a obtenção dos resultados disponível no apêndice A bem como outros códigos para os demais exemplos. Embora a padroniza- ção das análises estatísticas para os estudos de bioequivalência seja importante, não deve-se esperar que um modelo padrão ajuste-se a qualquer conjunto de dados originados destes tipo de estudos. Neste sentido, são apresentados alternativas que podem auxiliar o pesquisador na tomada de uma decisão em termos de bioequivalência media mais segura. / The interest in bioequivalence studies began in the early 1960s especially in the United States of America where the FDA was the rst regulatory agency to show interest upon this issue. In Brazil, this interest started in 1999 the year when a law regulated the generic drugs in the country. The ANVISA is the Brazilian regulatory agency responsible for inspecting the bioequivalence centers and giving guidelines for this issue. In general, a standard parametric model for the statistical step is indicated for the average bioequivalence decision and this model is expected to be tted by the data obtained in the bioequivalence studies. In some cases, this model would not be appropriate. In this way, this thesis proposes the use of more comprehensive parametric models based on other probability distributions for the average bioequivalence decision and that can model asymmetrical data, a common situation in bioequivalence studies. In addition, there is no need of a logarithmic transformation for the pharmacokinetic parameters which could aect the range of the bioequivalence limits. We also propose the use of parametrical bivariate models for the joint decision of the average bioequivalence decision, since these measures are usually analyzed simultaneously with two pharmacokinetic parameters. We use Bayesian methods to estimate the parameters, given the great exibility of this approach when combined with the use of MCMC methods using free available softwares. This thesis also presents a study of the empirical power of hypothesis testing for the proposed univariate models and four examples are introduced. In the examples one, two and three we apply the average bioequivalence decision and in the fourth example we consider for the implementation of population and individual bioequivalence. In the examples one, two and three were observed gains in the tting of the proposed new models for the data where some existing approaches were used in the selection criteria for the proposed models. Example four provides a standard analysis of population and individual bioequivalence with the computer code for obtaining the results available in the Appendix A, as well as other codes. Although the standardization of statistical analysis for bioequivalence studies is important, a standard model is not expected to be well tted to any data set originated by such studies. In this way, we present alternatives that can help researchers in making a decision in terms of average bioequivalence with more security.

Este trabalho tem como objetivo calcular intervalos de confiança para altos quantis oriundos de distribuições de caudas pesadas. Para isso, utilizamos os métodos da aproximação pela distribuição normal, razão de verossimilhanças, {\\it data tilting} e gama generalizada. Obtivemos, através de simulações, que os intervalos calculados a partir do método da gama generalizada apresentam probabilidades de cobertura bem próximas do nível de confiança, com amplitudes médias menores do que os outros três métodos, para dados gerados da distribuição Weibull. Todavia, para dados gerados da distribuição Fréchet, o método da razão de verossimilhanças fornece os melhores intervalos. Aplicamos os métodos utilizados neste trabalho a um conjunto de dados reais, referentes aos pagamentos de indenizações, em reais, de seguros de incêndio, de um determinado grupo de seguradoras no Brasil, no ano de 2003 / In this work, confidence intervals for high quantiles from heavy-tailed distributions were computed. More specifically, four methods, namely, normal approximation method, likelihood ratio method, data tilting method and generalised gamma method are used. A simulation study with data generated from Weibull distribution has shown that the generalised gamma method has better coverage probabilities with the smallest average length intervals. However, from data generated from Fréchet distribution, the likelihood ratio method gives the better intervals. Moreover, the methods used in this work are applied on a real data set from 1758 Brazilian fire claims

A distribuição simplex, proposta por Barndor-Nielsen e Jørgensen (1991) é útil para a modelagem de dados contínuos no intervalo (0,1). Nesse trabalho, desenvolve-se o modelo de regressão simplex considerando-se ´ = h(X; ¯), sendo h(:; :) uma função arbitr ária. Denem-se os resíduos para o modelo considerado e obtêm-se correções assintóticas para resíduos do tipo Ri. A primeira correção proposta baseou-se na obtenção da expressão assintótica para a densidade dos resíduos de Pearson, corrigidos até ordem O(n¡1). Esses resíduos foram denidos de forma a terem a mesma distribuição dos resíduos verdadeiros de Pearson. Estudos de simulação mostraram que a distribuição empírica dos resíduos corrigidos pela densidade encontra-se mais próxima da distribuição dos verdadeiros resíduos de Pearson do que para o resíduo não corrigido de Pearson. A segunda correção proposta considera o método dos momentos. Geralmente, E(Ri) e Var(Ri) são diferentes de zero e um, respectivamente, por termos de ordem O(n¡1). Usando-se os resultados de Cox e Snell (1968), obtiveram-se as expressões aproximadas de ordem O(n¡1) para E(Ri) e Var(Ri). Um estudo de simulação está sendo realizado para avaliação da técnica proposta. A técnica desenvolvida no primeiro estudo, foi aplicada a dois conjuntos de dados, sendo o primeiro deles, dados sobre oxidação de amônia, considerando-se preditor linear e o outro sobre porcentagem de massa seca (MS) em grãos de milho, considerando-se preditor linear e não linear. Os resultados obtidos para os dados de oxidação de amônia, indicaram que o modelo com preditor linear está bem ajustado aos dados, considerando-se a exclusão de alguns possíveis pontos inuentes, sendo que a correção proposta, para a densidade dos resíduos, apresenta os melhores resultados. Observando-se os resultados para os dados de massa seca, os melhores resultados foram obtidos, considerando-se um dos modelos com preditor não linear. / The simplex distribution, proposed by Barndor-Nielsen e Jørgensen (1991) is useful for modeling continuous data in the (0,1) interval. In this work, we developed the simplex regression model, considering ´ = h(X; ¯), where h(:; :) is an arbitrary function. We dened the residuals to this model and obtained asymptotic corrections to residuals of the type Ri. The rst correction proposed, was based in obtaining the asymptotic expression for the density of Pearson residuals, corrected to order O(n¡1). These residuals were dened in order to have the same distribution of true Pearson residuals. Simulation studies showed that the empirical distribution of the modied residuals is closer to the distribution of the true Pearson residuals than the unmodied Pearson residuals. The second one, considers the method of moments. Generally E(Ri) and Var(Ri) are dierent from zero and one, respectively, by terms of order O(n¡1). Using the results of Cox and Snell (1968), we obtained the approximate expressions of order O(n¡1) for E(Ri) and Var(Ri). A simulation study is being conducted to evaluate the proposed technique. We applied the techniques in two data sets, the rst one, is a dataset of ammonia oxidation, considering linear predictor and the other one was the percentage of dry matter in maize, considering linear predictor and nonlinear. The results obtained for the oxidation ammonia data indicated that the model considering linear predictor, tted well to the data, if we consider the exclusion of some possible inuential points. The proposed correction for the density of Pearson residuals, showed better results. Observing the results for the dry matter data, the best results were obtained for a model with a specied nonlinear predictor.