A nova família de distribuições odd log-logística: teoria e aplicações

Neste trabalho, foi proposta uma nova família de distribuições, a qual permite modelar dados de sobrevivência quando a função de risco tem formas unimodal e U (banheira). Ainda, foram consideradas as modificações das distribuições Weibull, Fréchet, half-normal generalizada, log-logística e lognormal. Tomando dados não-censurados e censurados, considerou-se os estimadores de máxima verossimilhança para o modelo proposto, a fim de verificar a flexibilidade da nova família. Além disso, um modelo de regressão locação-escala foi utilizado para verificar a influência de covariáveis nos tempos de sobrevida. Adicionalmente, conduziu-se uma análise de resíduos baseada nos resíduos deviance modificada. Estudos de simulação, utilizando-se de diferentes atribuições dos parâmetros, porcentagens de censura e tamanhos amostrais, foram conduzidos com o objetivo de verificar a distribuição empírica dos resíduos tipo martingale e deviance modificada. Para detectar observações influentes, foram utilizadas medidas de influência local, que são medidas de diagnóstico baseadas em pequenas perturbações nos dados ou no modelo proposto. Podem ocorrer situações em que a suposição de independência entre os tempos de falha e censura não seja válida. Assim, outro objetivo desse trabalho é considerar o mecanismo de censura informativa, baseado na verossimilhança marginal, considerando a distribuição log-odd log-logística Weibull na modelagem. Por fim, as metodologias descritas são aplicadas a conjuntos de dados reais.

(Table 1) Mean grain sizes and standard deviations of gas hydrate samples

Methane hydrates are present in marine seep systems and occur within the gas hydrate stability zone. Very little is known about their crystallite sizes and size distributions because they are notoriously difficult to measure. Crystal size distributions are usually considered as one of the key petrophysical parameters because they influence mechanical properties and possible compositional changes, which may occur with changing environmental conditions. Variations in grain size are relevant for gas substitution in natural hydrates by replacing CH4 with CO2 for the purpose of carbon dioxide sequestration. Here we show that crystallite sizes of gas hydrates from some locations in the Indian Ocean, Gulf of Mexico and Black Sea are in the range of 200-400 µm; larger values were obtained for deeper-buried samples from ODP Leg 204. The crystallite sizes show generally a log-normal distribution and appear to vary sometimes rapidly with location.

(Table 1) Crystal sizes of measured samples

Due to experimental difficulties grain size distributions of gas hydrate crystallites are largely unknown in natural samples. For the first time, we were able to determine grain size distributions of six natural gas hydrates for samples retrieved from the Gulf of Mexico and from Hydrate Ridge offshore Oregon from varying depths. High-energy synchrotron radiation provides high photon fluxes as well as high penetration depth and thus allows for investigation of bulk sediment samples. The gas hydrate crystallites appear to be (log-) normally distributed in the natural samples and to be of roughly globular shape. The mean grain sizes are in the range from 300-600 µm with a tendency for bigger grains to occur in greater depth, possibly indicating a difference in the formation age. Laboratory produced methane hydrate, starting from ice and aged for 3 weeks, shows half a log-normal curve with a mean value of ~40 µm. This one order-of-magnitude smaller grain sizes suggests that care must be taken when transposing grain-size sensitive (petro-)physical data from laboratory-made gas hydrates to natural settings.

(Table 1) Crystal sizes of measured samples from the Bush Hill region in the Gulf of Mexico and from ODP Leg 204 at the Hydrate Ridge offshore Oregon

The grain sizes of gas hydrate crystallites are largely unknown in natural samples. Single grains are hardly detectable with electron or optical microscopy. For the first time, we have used high-energy synchrotron diffraction to determine grain sizes of six natural gas hydrates retrieved from the Bush Hill region in the Gulf of Mexico and from ODP Leg 204 at the Hydrate Ridge offshore Oregon from varying depth between 1 and 101 metres below seafloor. High-energy synchrotron radiation provides high photon fluxes as well as high penetration depth and thus allows for investigation of bulk sediment samples. Gas hydrate grain sizes were measured at the Beam Line BW 5 at the HASYLAB/Hamburg. A 'moving area detector method', originally developed for material science applications, was used to obtain both spatial and orientation information about gas hydrate grains within the sample. The gas hydrate crystal sizes appeared to be (log-)normally distributed in the natural samples. All mean grain sizes lay in the range from 300 to 600 µm with a tendency for bigger grains to occur in greater depth. Laboratory-produced methane hydrate, aged for 3 weeks, showed half a log-normal curve with a mean grain size value of c. 40 µm. The grains appeared to be globular shaped.

Geochemistry, grain sizes and radiocarbon age of sediment core Lz1005 from Amery Oasis, East Antarctica

The clay mineralogical composition of a 552 cm long sediment core from Lake Terrasovoje in Amery Oasis, East Antarctica, was analysed and compared with that in surface sediments from other locations in the vicinity. The lower part of the sediment core is formed by sub- and proglacial sediments with a dominance of smectite and illite, and lower amounts of kaolinite and chlorite. The upper part of the core is deposited after 12 500 cal yr bp and mainly composed of illite and kaolinite, with low amounts of smectite and chlorite, such as found in samples from rock outcrops and covering sediments throughout Amery Oasis. The clay composition in the lower section of core Lz1005 suggest that the basin of Lake Terrasovoje was filled by a 150-200 m thickened Nemesis Glacier prior to 12 500 cal yr bp rather than by local ice caps.

(Table 1) Mean sizes of Hydrobia ulvae juveniles in the littoral zone of the Chernaya Inlet (Kandalaksha Bay, White Sea) in July-September 1995

Based on observations and experiments carried out within the White Sea silty-sandy littoral zone in 1994-1997 data on biology of development and behavior of Hydrobia ulvae juveniles over water column and in sediments were obtained. Hydrobiid juveniles 0.125-0.150 mm in size appear in plankton during the second half of June and in two to three weeks they precipitate on sediments reaching 0.300-0.350 mm in size. Specific biological features of the White Sea hydrobiids are a short reproductive period and a short period of juvenile growth related to long under-ice time and decelerated warming of shallow waters. Distribution of juvenile individuals of H. ulvae is primarily determined by hydrodynamics and microtopography of the littoral zone. Redistribution of the juveniles permanently takes place, since all size groups of the juveniles are equally subjected to migration. During the first few weeks after settling mortality of juvenile mudsnails is 85%.