957 resultados para Probability distributions
Resumo:
Esta dissertação aplica a regularização por entropia máxima no problema inverso de apreçamento de opções, sugerido pelo trabalho de Neri e Schneider em 2012. Eles observaram que a densidade de probabilidade que resolve este problema, no caso de dados provenientes de opções de compra e opções digitais, pode ser descrito como exponenciais nos diferentes intervalos da semireta positiva. Estes intervalos são limitados pelos preços de exercício. O critério de entropia máxima é uma ferramenta poderosa para regularizar este problema mal posto. A família de exponencial do conjunto solução, é calculado usando o algoritmo de Newton-Raphson, com limites específicos para as opções digitais. Estes limites são resultados do princípio de ausência de arbitragem. A metodologia foi usada em dados do índice de ação da Bolsa de Valores de São Paulo com seus preços de opções de compra em diferentes preços de exercício. A análise paramétrica da entropia em função do preços de opções digitais sínteticas (construídas a partir de limites respeitando a ausência de arbitragem) mostraram valores onde as digitais maximizaram a entropia. O exemplo de extração de dados do IBOVESPA de 24 de janeiro de 2013, mostrou um desvio do princípio de ausência de arbitragem para as opções de compra in the money. Este princípio é uma condição necessária para aplicar a regularização por entropia máxima a fim de obter a densidade e os preços. Nossos resultados mostraram que, uma vez preenchida a condição de convexidade na ausência de arbitragem, é possível ter uma forma de smile na curva de volatilidade, com preços calculados a partir da densidade exponencial do modelo. Isto coloca o modelo consistente com os dados do mercado. Do ponto de vista computacional, esta dissertação permitiu de implementar, um modelo de apreçamento que utiliza o princípio de entropia máxima. Três algoritmos clássicos foram usados: primeiramente a bisseção padrão, e depois uma combinação de metodo de bisseção com Newton-Raphson para achar a volatilidade implícita proveniente dos dados de mercado. Depois, o metodo de Newton-Raphson unidimensional para o cálculo dos coeficientes das densidades exponenciais: este é objetivo do estudo. Enfim, o algoritmo de Simpson foi usado para o calculo integral das distribuições cumulativas bem como os preços do modelo obtido através da esperança matemática.
Resumo:
Water currents are vertically structured in many marine systems and as a result, vertical movements by fish larvae and zooplankton affect horizontal transport (Power, 1984). In estuaries, the vertical movements of larvae with tidal periods can result in their retention or ingress (Fortier and Leggett, 1983; Rijnsdorp et al., 1985; Cronin and Forward, 1986; Forward et al., 1999). On the continental shelf, the vertical movements of organisms interact daily and ontogenetically with depth-varying currents to affect horizontal transport (Pillar et al., 1989; Barange and Pillar, 1992; Cowen et al., 1993, 2000; Batchelder et al., 2002).
Resumo:
Population assessments seldom incorporate habitat information or use previously observed distributions of fish density. Because habitat affects the spatial distribution of fish density and overall abundance, the use of habitat information and previous estimates of fish density can produce more precise and less biased population estimates. In this study, we describe how poststratification can be applied as an unbiased estimator to data sets that were collected under a probability sampling design, typical of many multispecies trawl surveys. With data from a multispecies survey of juvenile flatfish, we show how poststratification can be applied to a data set that was not collected under a probability sampling design, where both the precision and the bias are unknown. For each of four species, three estimates of total abundance were compared: 1) unstratified; 2) poststratified by habitat; and 3) poststratified by habitat and fish density (high fish density and low fish density) in nearby years. Poststratification by habitat gave more precise and (or) less design-biased estimates than an unstratified estimator for all species in all years. Poststratification by habitat and fish density produced the most precise and representative estimates when the sample size in the high fish-density and low fish-density strata were sufficient (in this study, n≥20 in the high fish-density stratum, n≥9 in the low fish-density stratum). Because of the complexities of statistically testing the annual stratified data, we compared three indices of abundance for determining statistically significant changes in annual abundance. Each of the indices closely approximated the annual differences of the poststratified estimates. Selection of the most appropriate index was dependent upon the species’ density distribution within habitat and the sample size in the different habitat areas. The methods used in this study are particularly useful for estimating individual species abundance from multispecies surveys and for retrospective st
Resumo:
Inter and intra-annual variation in year-class strength was analyzed for San Francisco Bay Pacific herring (Clupea pallasi) by using otoliths of juveniles. Juvenile herring were collected from March through June in 1999 and 2000 and otoliths from subsamples of these collections were aged by daily otolith increment analysis. The composition of the year classes in 1999 and 2000 were determined by back-calculating the birth date distribution for surviving juvenile herring. In 2000, 729% more juveniles were captured than in 1999, even though an estimated 12% fewer eggs were spawned in 2000. Spawning-date distributions show that survival for the 2000 year class was exceptionally good for a short (approximately 1 month) period of spawning, resulting in a large abundance of juvenile recruits. Analysis of age at size shows that growth rate increased significantly as the spawning season progressed both in 1999 and 2000. However, only in 2000 were the bulk of surviving juveniles a product of the fast growth period. In the two years examined, year-class strength was not predicted by the estimated number of eggs spawned, but rather appeared to depend on survival of eggs or larvae (or both) through the juvenile stage. Fast growth through the larval stage may have little effect on year-class strength if mortality during the egg stage is high and few larvae are available.
Resumo:
Size distribution within re- ported landings is an important aspect of northern Gulf of Mexico penaeid shrimp stock assessments. It reflects shrimp population characteristics such as numerical abundance of various sizes, age structure, and vital rates (e.g. recruitment, growth, and mortality), as well as effects of fishing, fishing power, fishing practices, sampling, size-grading, etc. The usual measure of shrimp size in archived landings data is count (C) the number of shrimp tails (abdomen or edible portion) per pound (0.4536 kg). Shrimp are marketed and landings reported in pounds within tail count categories. Statistically, these count categories are count class intervals or bins with upper and lower limits expressed in C. Count categories vary in width, overlap, and frequency of occurrence within the landings. The upper and lower limits of most count class intervals can be transformed to lower and upper limits (respectively) of class intervals expressed in pounds per shrimp tail, w, the reciprocal of C (i.e. w = 1/C). Age based stock assessments have relied on various algorithms to estimate numbers of shrimp from pounds landed within count categories. These algorithms required un- derlying explicit or implicit assumptions about the distribution of C or w. However, no attempts were made to assess the actual distribution of C or w. Therefore, validity of the algorithms and assumptions could not be determined. When different algorithms were applied to landings within the same size categories, they produced different estimates of numbers of shrimp. This paper demonstrates a method of simulating the distribution of w in reported biological year landings of shrimp. We used, as examples, landings of brown shrimp, Farfantepenaeus aztecus, from the northern Gulf of Mexico fishery in biological years 1986–2006. Brown shrimp biological year, Ti, is defined as beginning on 1 May of the same calendar year as Ti and ending on 30 April of the next calendar year, where subscript i is the place marker for biological year. Biological year landings encompass most if not all of the brown shrimp life cycle and life span. Simulated distributions of w reflect all factors influencing sizes of brown shrimp in the landings within a given biological year. Our method does not require a priori assumptions about the parent distributions of w or C, and it takes into account the variability in width, overlap, and frequency of occurrence of count categories within the landings. Simulated biological year distributions of w can be transformed to equivalent distributions of C. Our method may be useful in future testing of previously applied algorithms and development of new estimators based on statistical estimation theory and the underlying distribution of w or C. We also examine some applications of biological year distributions of w, and additional variables derived from them.