Weiyan Ge. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 64-68). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction of Power Control Problem --- p.2 / Chapter 1.1.1 --- Classification of Power Control Problem --- p.2 / Chapter 1.1.2 --- Previous Works --- p.7 / Chapter 1.2 --- Scope and Contribution of the Thesis --- p.11 / Chapter 1.3 --- Organization of the Thesis --- p.12 / Chapter 2 --- Background --- p.14 / Chapter 2.1 --- Stochastic Approximation --- p.14 / Chapter 2.2 --- Lognormal Distribution --- p.17 / Chapter 2.2.1 --- Definition and Properties --- p.17 / Chapter 2.2.2 --- Application on Radio Propagation --- p.18 / Chapter 3 --- System Model and Centralized Algorithm --- p.21 / Chapter 3.1 --- System Model --- p.21 / Chapter 3.2 --- Problem Statement and the Centralized Algorithm --- p.25 / Chapter 4 --- Proposed Stochastic Power Control Algorithm --- p.30 / Chapter 4.1 --- Proposed Power Control Algorithm --- p.30 / Chapter 4.2 --- Basic Properties of the Algorithm --- p.33 / Chapter 4.3 --- Convergence Property --- p.38 / Chapter 5 --- Numerical Results --- p.44 / Chapter 5.1 --- Simulation Model --- p.44 / Chapter 5.2 --- Numerical Results --- p.47 / Chapter 6 --- Conclusions And Future Works --- p.58 / Chapter 6.1 --- Conclusions --- p.58 / Chapter 6.2 --- Future Works --- p.60 / Chapter A --- Basic Properties of LOG-Distribution --- p.62 / Bibliography --- p.64

This thesis work concerns about the Performance evolution of peer to peer networks, where we used different distribution technique’s of peer distribution like Weibull, Lognormal and Pareto distribution process. Then we used a network simulator to evaluate the performance of these three distribution techniques.During the last decade the Internet has expanded into a world-wide network connecting millions of hosts and users and providing services for everyone. Many emerging applications are bandwidth-intensive in their nature; the size of downloaded files including music and videos can be huge, from ten megabits to many gigabits. The efficient use of network resources is thus crucial for the survivability of the Internet. Traffic engineering (TE) covers a range of mechanisms for optimizing operational networks from the traffic perspective. The time scale in traffic engineering varies from the short-term network control to network planning over a longer time period.Here in this thesis work we considered the peer distribution technique in-order to minimise the peer arrival and service process with three different techniques, where we calculated the congestion parameters like blocking time for each peer before entering into the service process, waiting time for a peers while the other peer has been served in the service block and the delay time for each peer. Then calculated the average of each process and graphs have been plotted using Matlab to analyse the results

The Black-Scholes option pricing model has several well recognized deficiencies, one of which is its assumption of a constant and time-homogeneous stock return volatility term. The implied volatility smile has been studied by subsequent researchers and various models have been developed in an attempt to reproduce this phenomenon from within the models. However, few of these models yield closed-form pricing formulas that are easy to implement in practice. In this thesis, we study a Mixture Lognormal model (MLN) for European option pricing, which assumes that future stock prices are conditionally described by a mixture of lognormal distributions. The ability of mixture models in generating volatility smiles as well as delivering pricing improvement over the traditional Black-Scholes framework have been much researched under multi-component mixtures for many derivatives and high-volatility individual stock options. In this thesis, we investigate the performance of the model under the simplest two-component mixture in a market characterized by relative tranquillity and over a relatively stable period for broad-based index options. A careful interpretation is given to the model and the results obtained in the thesis. This di erentiates our study from many previous studies on this subject. Throughout the thesis, we establish the unique advantage of the MLN model, which is having closed-form option pricing formulas equal to the weighted mixture of Black-Scholes option prices. We also propose a robust calibration methodology to fit the model to market data. Extreme market states, in particular the so-called crash-o-phobia effect, are shown to be well captured by the calibrated model, albeit small pricing improvements are made over a relatively stable period of index option market. As a major contribution of this thesis, we extend the MLN model to price exotic options including binary, Asian, and barrier options. Closed-form formulas are derived for binary and continuously monitored barrier options and simulation-based pricing techniques are proposed for Asian and discretely monitored barrier options. Lastly, comparative results are analysed for various strike-maturity combinations, which provides insights into the formulation of hedging and risk management strategies.

The Black-Scholes option pricing model has several well recognized deficiencies, one of which is its assumption of a constant and time-homogeneous stock return volatility term. The implied volatility smile has been studied by subsequent researchers and various models have been developed in an attempt to reproduce this phenomenon from within the models. However, few of these models yield closed-form pricing formulas that are easy to implement in practice. In this thesis, we study a Mixture Lognormal model (MLN) for European option pricing, which assumes that future stock prices are conditionally described by a mixture of lognormal distributions. The ability of mixture models in generating volatility smiles as well as delivering pricing improvement over the traditional Black-Scholes framework have been much researched under multi-component mixtures for many derivatives and high-volatility individual stock options. In this thesis, we investigate the performance of the model under the simplest two-component mixture in a market characterized by relative tranquillity and over a relatively stable period for broad-based index options. A careful interpretation is given to the model and the results obtained in the thesis. This di erentiates our study from many previous studies on this subject. Throughout the thesis, we establish the unique advantage of the MLN model, which is having closed-form option pricing formulas equal to the weighted mixture of Black-Scholes option prices. We also propose a robust calibration methodology to fit the model to market data. Extreme market states, in particular the so-called crash-o-phobia effect, are shown to be well captured by the calibrated model, albeit small pricing improvements are made over a relatively stable period of index option market. As a major contribution of this thesis, we extend the MLN model to price exotic options including binary, Asian, and barrier options. Closed-form formulas are derived for binary and continuously monitored barrier options and simulation-based pricing techniques are proposed for Asian and discretely monitored barrier options. Lastly, comparative results are analysed for various strike-maturity combinations, which provides insights into the formulation of hedging and risk management strategies.

Dissertação (Mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. / Made available in DSpace on 2012-10-18T21:57:45Z (GMT). No. of bitstreams: 1 141980.pdf: 252258 bytes, checksum: a19f61f94801ffc8c5c5ec70ec0ebe33 (MD5)

>Magister Scientiae - MSc / There exists an extensive statistics literature dealing with non-parametric deconvolution, the estimation of the underlying population probability density when sample values are subject to measurement errors. In parametric deconvolution, on the other hand, the data are known to be from a specific distribution. In this case the parameters of the distribution can be estimated by e.g. maximum likelihood. In realistic cases the measurement errors may be heteroscedastic and there may be unknown parameters associated with the distribution. The specific realistic case is investigated in which the measurement error standard deviation is proportional to the true sample values. In this case it is shown that the method of moment’s estimation is particularly simple. Estimation by maximum likelihood is computationally very expensive, since numerical integration needs to be performed for each data point, for each evaluation of the likelihood function. Method of moment’s estimation sometimes fails to give physically meaningful estimates. The origin of this problem lies in the large sampling variations of the third moment. Possible remedies are considered. Due to the fact that a convolution integral needed to be calculated for each data point, and that this has to be repeated for each iteration towards the solution, maximum likelihood computing cost is very high. New preliminary work suggests that saddle point approximations could sometimes be used for the convolution integrals. This allows much larger datasets to be dealt with. Application of the theory is illustrated with simulation and real data.

The lognormal distribution is useful in modeling continuous random variables which are greater than or equal to zero. Example scenarios in which the lognormal distribution is used include, among many others: in medicine, latent periods of infectious diseases; in environmental science, the distribution of particles, chemicals, and organisms in the environment; in linguistics, the number of letters per word and the number of words per sentence; and in economics, age of marriage, farm size, and income. The lognormal distribution is also useful in modeling data which would be considered normally distributed except for the fact that it may be more or less skewed (Limpert, Stahel, and Abbt 2001). Appropriately estimating the parameters of the lognormal distribution is vital for the study of these and other subjects. Depending on the values of its parameters, the lognormal distribution takes on various shapes, including a bell-curve similar to the normal distribution. This paper contains a simulation study concerning the effectiveness of various estimators for the parameters of the lognormal distribution. A comparison is made between such parameter estimators as Maximum Likelihood estimators, Method of Moments estimators, estimators by Serfling (2002), as well as estimators by Finney (1941). A simulation is conducted to determine which parameter estimators work better in various parameter combinations and sample sizes of the lognormal distribution. We find that the Maximum Likelihood and Finney estimators perform the best overall, with a preference given to Maximum Likelihood over the Finney estimators because of its vast simplicity. The Method of Moments estimators seem to perform best when σ is less than or equal to one, and the Serfling estimators are quite accurate in estimating μ but not σ in all regions studied. Finally, these parameter estimators are applied to a data set counting the number of words in each sentence for various documents, following which a review of each estimator's performance is conducted. Again, we find that the Maximum Likelihood estimators perform best for the given application, but that Serfling's estimators are preferred when outliers are present.

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Made available in DSpace on 2017-07-10T19:24:36Z (GMT). No. of bitstreams: 1 Cacea Furlan Maggi.pdf: 2357763 bytes, checksum: f687985074f0d2f2b97598158d904ab2 (MD5) Previous issue date: 2006-02-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The objective of the present study compare the models of estimation of evapotranspiration of Reference (ETo) was adjusted of probabilistic Gama, Lognoral, and generalization distribution of extreme value, solver behind of Camargo, on Paraná West and to determine the wet availability index. The dados was obtained in IAPAR (Paraná Institute Agronomy) end SIMEPAR (Paraná Meteorology System). Worked of medium month temperature dados of Paraná regions, with geographic localization 24º14 00 latitude S to 25º27 00 and 53º07 00 to 54º24 00 longitude W far from Greenwch. The historic series done showed dados of 6 to 32 year of month medium temperature. The month medium temperature was used for solver of ETo. With of month dados was adjusted of probabilistic models associate of 75% occur. For to tried of probabilistic Gama and Lognormal models was to used adherences test of Kolmogorov-Smirnov, with 5% of probability. For GEV distribution of qualify of adjusted was available of Wang test of 5% probability. This values of P75 was used for wet availability index. The result was probabilistic Gama and Lognormal model showed similar comportment with to estimative of ETo, therefore all 144 series studied was accept of Kolmigorov-Smirnov adherence test, until of station with a few year of register adjusted, consequently the two models adjusted correct the ETo dados. The GEV model of 144 series available, 22 don t was accept of Wang test of 5% probability. On wet availability index showed variation of 0.33 to 1.33, how reference for wet availability analyses that valor less of 0.33 are to point out of deficit end tall of 1.33 wet excess. The results showed of June was the month the most valor of IDUs, was in this month too of occur better station number with wet excess, the 12 station available, 8 showed wet excess in this month. Was possible do see the most valor os IDUs happened in regions next, in São Miguel do Iguaçu and Foz do Iguaçu. All the series available don t shoed wet deficit. / O presente trabalho teve como objetivo comparar os modelos de estimativa de Evapotranspiração de Referência (ETo) Gama, Lognormal, e o modelo de distribuição generalizada de valores extremos (GEV), calculada através do modelo de Camargo, na região Oeste do Paraná e determinar o Índice de Disponibilidade de Umidade IDU. Os dados climáticos foram obtidos através do IAPAR (Instituto Agronômico do Paraná) e do SIMEPAR (Sistema Meteorológico do Paraná). Trabalhou-se com dados de temperatura média mensal da região Oeste do Paraná, cuja localização geográfica das estas estações se encontram entre - latitude: 24º17 00 a 25º27 00 S, e longitude: 53º07 00 a 54º24 00 W de Greenwch. As séries históricas utilizadas apresentavam dados de 6 a 32 anos de temperatura média mensal. Os dados de temperatura média mensal foram utilizados para calcular a Eto. A partir dos dados Eto mensais procedeu-se a verificação do ajuste dos modelos probabilísticos associados ao nível de 75% de ocorrência. Para a validação para os modelos probabilístico Gama e Lognormal foram utilizados testes de aderência de Kolmogorov- Smirnov, com significância de 5% de probabilidade. Para a distribuição GEV a qualidade do ajuste foi avaliada através do teste de Wang ao nível de 5% de probabilidade. Os valores do P75 utilizados P75 foram utilizados para o cálculo do Índice de Disponibilidade de Umidade. Os resultados foram que os modelos probabilísticos Gama e Lognomal apresentaram comportamentos semelhantes com relação à estimativa de Eto, pois todas as 144 séries estudadas todas foram aceitas pelo teste de aderência de Kolmogorov-Smirnov, até mesmo as estações com poucos anos de registros se ajustaram, portanto os dois modelos ajustam adequadamente os dados de Eto. Para o modelo GEV das 144 séries avaliadas 22 séries não foram aceitas pelo teste de Wang para o nível de 5% de probabilidade. Na determinação do Índice de Disponibilidade de Umidade que indica a variação de 0,33 £ IDU £ 1,33, como referência para a análise da disponibilidade de umidade, sendo que valores abaixo de 0,33 são indicações de déficit e acima de 1,33 de excesso hídrico. Os resultados mostram que no mês de junho foi o mês que apresentou os maiores valores de IDUs, foi neste mês também o que se verificou o maior número de estações com excesso hídrico, das 12 estações avaliadas 8 apresentaram excesso hídrico neste mês. Foi possível se verificar que os maiores valores de IDUs ocorreram em regiões próximas, que foram as regiões de São Miguel do Iguaçu e Foz do Iguaçu. Em todas as séries avaliadas, nenhuma apresentou déficit hídrico.

Made available in DSpace on 2017-05-12T14:47:59Z (GMT). No. of bitstreams: 1 Cacea Furlan Maggi.pdf: 2357763 bytes, checksum: f687985074f0d2f2b97598158d904ab2 (MD5) Previous issue date: 2006-02-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The objective of the present study compare the models of estimation of evapotranspiration of Reference (ETo) was adjusted of probabilistic Gama, Lognoral, and generalization distribution of extreme value, solver behind of Camargo, on Paraná West and to determine the wet availability index. The dados was obtained in IAPAR (Paraná Institute Agronomy) end SIMEPAR (Paraná Meteorology System). Worked of medium month temperature dados of Paraná regions, with geographic localization 24º14 00 latitude S to 25º27 00 and 53º07 00 to 54º24 00 longitude W far from Greenwch. The historic series done showed dados of 6 to 32 year of month medium temperature. The month medium temperature was used for solver of ETo. With of month dados was adjusted of probabilistic models associate of 75% occur. For to tried of probabilistic Gama and Lognormal models was to used adherences test of Kolmogorov-Smirnov, with 5% of probability. For GEV distribution of qualify of adjusted was available of Wang test of 5% probability. This values of P75 was used for wet availability index. The result was probabilistic Gama and Lognormal model showed similar comportment with to estimative of ETo, therefore all 144 series studied was accept of Kolmigorov-Smirnov adherence test, until of station with a few year of register adjusted, consequently the two models adjusted correct the ETo dados. The GEV model of 144 series available, 22 don t was accept of Wang test of 5% probability. On wet availability index showed variation of 0.33 to 1.33, how reference for wet availability analyses that valor less of 0.33 are to point out of deficit end tall of 1.33 wet excess. The results showed of June was the month the most valor of IDUs, was in this month too of occur better station number with wet excess, the 12 station available, 8 showed wet excess in this month. Was possible do see the most valor os IDUs happened in regions next, in São Miguel do Iguaçu and Foz do Iguaçu. All the series available don t shoed wet deficit. / O presente trabalho teve como objetivo comparar os modelos de estimativa de Evapotranspiração de Referência (ETo) Gama, Lognormal, e o modelo de distribuição generalizada de valores extremos (GEV), calculada através do modelo de Camargo, na região Oeste do Paraná e determinar o Índice de Disponibilidade de Umidade IDU. Os dados climáticos foram obtidos através do IAPAR (Instituto Agronômico do Paraná) e do SIMEPAR (Sistema Meteorológico do Paraná). Trabalhou-se com dados de temperatura média mensal da região Oeste do Paraná, cuja localização geográfica das estas estações se encontram entre - latitude: 24º17 00 a 25º27 00 S, e longitude: 53º07 00 a 54º24 00 W de Greenwch. As séries históricas utilizadas apresentavam dados de 6 a 32 anos de temperatura média mensal. Os dados de temperatura média mensal foram utilizados para calcular a Eto. A partir dos dados Eto mensais procedeu-se a verificação do ajuste dos modelos probabilísticos associados ao nível de 75% de ocorrência. Para a validação para os modelos probabilístico Gama e Lognormal foram utilizados testes de aderência de Kolmogorov- Smirnov, com significância de 5% de probabilidade. Para a distribuição GEV a qualidade do ajuste foi avaliada através do teste de Wang ao nível de 5% de probabilidade. Os valores do P75 utilizados P75 foram utilizados para o cálculo do Índice de Disponibilidade de Umidade. Os resultados foram que os modelos probabilísticos Gama e Lognomal apresentaram comportamentos semelhantes com relação à estimativa de Eto, pois todas as 144 séries estudadas todas foram aceitas pelo teste de aderência de Kolmogorov-Smirnov, até mesmo as estações com poucos anos de registros se ajustaram, portanto os dois modelos ajustam adequadamente os dados de Eto. Para o modelo GEV das 144 séries avaliadas 22 séries não foram aceitas pelo teste de Wang para o nível de 5% de probabilidade. Na determinação do Índice de Disponibilidade de Umidade que indica a variação de 0,33 £ IDU £ 1,33, como referência para a análise da disponibilidade de umidade, sendo que valores abaixo de 0,33 são indicações de déficit e acima de 1,33 de excesso hídrico. Os resultados mostram que no mês de junho foi o mês que apresentou os maiores valores de IDUs, foi neste mês também o que se verificou o maior número de estações com excesso hídrico, das 12 estações avaliadas 8 apresentaram excesso hídrico neste mês. Foi possível se verificar que os maiores valores de IDUs ocorreram em regiões próximas, que foram as regiões de São Miguel do Iguaçu e Foz do Iguaçu. Em todas as séries avaliadas, nenhuma apresentou déficit hídrico.