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Deformação harmônica da triangulação de Delaunay / Harmonic deformation of the Delaunay triangulationRafael de Mattos Grisi 28 August 2009 (has links)
Dado um processo de Poisson d-dimensional, construímos funções harmônicas na triangulação de Delaunay associada, com comportamento assintótico linear, como limite de um processo de harness sem ruído. Tais funções permitem que construamos uma nova imersão da triangulação de Delaunay, que denominaremos de deformação harmônica. / Given a d-dimensional Poisson point process, we construct harmonic functions on the associated Delaunay triangulation, with linear assymptotic behaviour, as the limit of a noiseless harness process. These mappings allow us to find a new embedding for the Delaunay triangulation. We call it harmonic deformation of the graph.
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巨災風險債券之計價分析 / Pricing Catastrophe Risk Bonds吳智中, Wu, Chih-Chung Unknown Date (has links)
運用傳統再保險契約移轉風險受限於承保能量的逐年波動,尤其自90年代起,全球巨災頻繁,保險人損失巨幅增加,承保能量急遽萎縮,基於巨災市場之資金需求,再保險轉向資本市場,預期將巨災風險移轉至投資人,促成保險衍生性金融商品之創新,本研究針對佔有顯著交易量的巨災風險債券進行分析,基於Cummins和Geman (1995)所建構巨災累積損失模型,引用Duffie 與Singleton (1999)於違約債券的計價模式,將折現利率表示為短期利率加上事故發生率及預期損失比例之乘積,並將債券期間延長至多年期,以符合市場承保的需求,應用市場無套利假設及平賭測度計價的方法計算合理的市場價值,巨災損失過程將分成損失發展期與損失確定期,以卜瓦松過程表示巨災發生頻率,並利用台灣巨災經驗資料建立合適之損失幅度模型,最後以蒙地卡羅方法針對三種不同型態的巨災風險債券試算合理價值,並具體結論所得的數值結果與後續之研究建議。 / Using traditional reinsurance treaties to transfer insurance risks are restrained due to the volatility of the underwriting capacity annually. Catastrophe risks have substantially increased since the early 1990s and have directly resulted significant claim losses for the insurers. Hence the insurers are pursuing the financial capacities from the capital market. Transferring the catastrophe risks to the investor have stimulated the financial innovation for the insurance industry. In this study, pricing issues for the heavily traded catastrophe risk bonds (CAT-bond) are investigated. The aggregated catastrophe loss model in Cummins and Geman (1995) are adopted. While the financial techniques in valuing the defaultable bonds in Duffie and Singleton (1999) are employed to determine the fair prices incorporating the claim hazard rates and the loss severity. The duration of the CAT-bonds is extended from single year to multiple years in order to meet the demand from the reinsurance market. Non- arbitrage theory and martingale measures are employed to determine their fair market values. The contract term of the CAT-bonds is divided into the loss period and the development period. The frequency of the catastrophe risk is modeled through the Poisson process. Taiwan catastrophe loss experiences are examined to build the plausible loss severity model. Three distant types of CAT-bonds are analyzed through Monte Carlo method for illustrations. This paper concludes with remarks regarding some pricing issues of CAT-bonds.
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A Study of Gamma Distributions and Some Related WorksChou, Chao-Wei 11 May 2004 (has links)
Characterization of distributions has been an important topic in statistical theory for decades. Although there have been many well known results already developed, it is still of great interest to find new characterizations of commonly used distributions in application, such as normal or gamma distribution. In practice, sometimes we make guesses on the distribution to be fitted to the data observed, sometimes we use the characteristic properties of those distributions to do so. In this paper we will restrict our attention to the characterizations of gamma distribution as well as some related studies on the corresponding parameter estimation based on the characterization properties. Some simulation studies are also given.
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O processo de Poisson estendido e aplicações. / O processo de Poisson estendido e aplicações.Salasar, Luis Ernesto Bueno 14 June 2007 (has links)
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Previous issue date: 2007-06-14 / Financiadora de Estudos e Projetos / Abstract
In this dissertation we will study how extended Poisson process can be applied to
construct discrete probabilistic models. An Extended Poisson Process is a continuous
time stochastic process with the state space being the natural numbers, it is obtained
as a generalization of homogeneous Poisson process where transition rates depend on
the current state of the process. From its transition rates and Chapman-Kolmogorov
di¤erential equations, we can determine the probability distribution at any …xed time of
the process. Conversely, given any probability distribution on the natural numbers, it
is possible to determine uniquely a sequence of transition rates of an extended Poisson
process such that, for some instant, the unidimensional probability distribution coincides
with the provided probability distribution. Therefore, we can conclude that extended
Poisson process is as a very ‡exible framework on the analysis of discrete data, since it
generalizes all probabilistic discrete models.
We will present transition rates of extended Poisson process which generate Poisson,
Binomial and Negative Binomial distributions and determine maximum likelihood estima-
tors, con…dence intervals, and hypothesis tests for parameters of the proposed models. We
will also perform a bayesian analysis of such models with informative and noninformative
prioris, presenting posteriori summaries and comparing these results to those obtained
by means of classic inference. / Nesta dissertação veremos como o proceso de Poisson estendido pode ser aplicado
à construção de modelos probabilísticos discretos. Um processo de Poisson estendido é
um processo estocástico a tempo contínuo com espaço de estados igual ao conjunto dos
números naturais, obtido a partir de uma generalização do processo de Poisson homogê-
neo onde as taxas de transição dependem do estado atual do processo. A partir das taxas
de transição e das equações diferenciais de Chapman-Kolmogorov pode-se determinar a
distribuição de probabilidades para qualquer tempo …xado do processo. Reciprocamente,
dada qualquer distribuição de probabilidades sobre o conjunto dos números naturais é pos-
sível determinar, de maneira única, uma seqüência de taxas de transição de um processo de
Poisson estendido tal que, para algum instante, a distribução unidimensional do processo
coincide com a dada distribuição de probabilidades. Portanto, o processo de Poisson es-
tendido se apresenta como uma ferramenta bastante ‡exível na análise de dados discretos,
pois generaliza todos os modelos probabilísticos discretos.
Apresentaremos as taxas de transição dos processos de Poisson estendido que ori-
ginam as distribuições de Poisson, Binomial e Binomial Negativa e determinaremos os
estimadores de máxima verossimilhança, intervalos de con…ança e testes de hipóteses dos
parâmetros dos modelos propostos. Faremos também uma análise bayesiana destes mod-
elos com prioris informativas e não informativas, apresentando os resumos a posteriori e
comparando estes resultados com aqueles obtidos via inferência clássica.
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Controle on-line por atributos para o n?mero de n?o-conformidades no item inspecionado com base em uma sequ?ncia de inspe??oRocha, Andre Luiz Sena da 29 December 2010 (has links)
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Previous issue date: 2010-12-29 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This paper proposes a procedure to control on-line processes for attributes, using an Shewhart
control chart with two control limits (warning limit and control limit) and will be based on a
sequence of inspection (h). The inspection procedure is based on Taguchi et al. (1989), in
which to inspect the item, if the number of non-conformities is higher than an upper control
limit, the process needs to be stopped and some adjustment is required; and, if the last
inspection h, from all items inspected present a number of non-conformities between the
control limit and warning limit. The items inspected will suffer destructive inspection, being
discarded after inspection. Properties of an ergodic Markov chain are used to get the
expression of average cost per item and the aim was the determination of four optimized
parameters: the sampling interval of the inspections (m); the constant W to draw the warning
limit (W); the constant C to draw the control limit (C), where W ? C, and the length of
sequence of inspections (h). Numerical examples illustrate the proposed procedure / Este trabalho prop?e um procedimento de controle on-line de processos por atributos,
utilizando um gr?fico de Shewhart com dois Limites de Controle (Limite de Advert?ncia e
Limite de Controle) e ser? baseado numa sequ?ncia de inspe??o (h). O procedimento de
inspe??o ? baseado em Taguchi et al. (1989). Assim, ao inspecionar o item, o processo ?
parado para ajuste se o n?mero de n?o conformidades for superior ao Limite de Controle;
como tamb?m se nas ?ltimas h inspe??es, todos os h itens inspecionados apresentarem um
n?mero de n?o-conformidades entre os Limites de Advert?ncia e de Controle. Utilizando-se
de propriedades de uma Cadeia de Markov Erg?dica, foi obtida uma express?o do custo
m?dio do sistema de controle, que pode ser minimizada por quatro par?metros: Intervalo entre
inspe??es (m), Limite de Advert?ncia (W), Limite de controle (C, em que W ≤ C) e o tamanho
da sequ?ncia de inspe??o (h). Um exemplo num?rico ilustra o procedimento proposto
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Modelo de confiabilidade para sistemas reparáveis considerando diferentes condições de manutenção preventiva imperfeita. / Reliability model to repairable system under different conditions for imperfect preventive maintenance.Marcos Antonio Coque Junior 06 October 2016 (has links)
Um sistema reparável opera sob uma estratégia de manutenção que exige ações de recuperação preventiva em tempos pré-definidos e ações de reparo quando ocorre a perda de função do sistema. A manutenção preventiva (MP) é programada periodicamente e muitas vezes possui um intervalo de tempo fixo para ações. No entanto, as atividades de MP podem não restaurar o sistema para uma condição similar ao início de vida deste, mas para uma situação intermediária. Nesse caso, a MP é denominada de imperfeita. Além disso, ao longo da vida do sistema, são executados diferentes planos de manutenção com condições e atividades distintas que podem afetar a intensidade de falha de diferentes maneiras. Para modelar essas características da MP em um sistema reparável, propõe-se uma nova classe de modelo de fator de melhoria, denominado fator de melhoria variável que possibilita a modelagem da situação de manutenção perfeita. A formulação da função de verossimilhança foi desenvolvida para estimação dos parâmetros bem como desenvolvidos testes de verificação da qualidade de ajuste, intervalos de confiança para os parâmetros e otimização da periodicidade de realização da MP com base no enfoque dos novos modelos propostos. Os resultados foram aplicados em dados reais e verificou-se uma parametrização mais flexível a MP imperfeita e maior versatilidade nas análises de confiabilidade do sistema quando utilizado os novos modelos. / A repairable system operates under a maintenance strategy that calls for preventive repair actions at prescheduled times and the repair actions that restore system when failure occurs. The preventive maintenance (PM) is scheduled periodically and it often holds a fixed time interval for PM actions. However, PM activities are generally imperfect and cannot restore the system to as good as new condition but to an intermediate situation, which is called imperfect PM. In addition, throughout system life are implemented diverse maintenance policies with different activities and conditions that may affect the failure intensity in different ways. To model these PM characteristics, proposes a new model class of improvement factor called variable improvement factor that also enables modeling perfect maintenance situation. The likelihood function is developed for parameter estimation as well as goodness-of-fit tests and confidence intervals for the parameters are developed, and optimization of the PM intervals based on the proposed models is presented. The proposed model was applied to a data set and a more flexible parameterization for imperfect PM and greater versatility in the system reliability analysis were verified with the use of the new model.
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Estimation paramétriques et tests d'hypothèses pour des modèles avec plusieurs ruptures d'un processus de poisson / Parametric estimation and hypothesis testing for models with multiple change-point of poisson processTop, Alioune 20 June 2016 (has links)
Ce travail est consacré aux problèmes d’estimation paramétriques, aux tests d’hypothèses et aux tests d’ajustement pour les processus de Poisson non homogènes.Tout d’abord on a étudié deux modèles ayant chacun deux sauts localisés par un paramètre inconnu. Pour le premier modèle la somme des sauts est positive. Tandis que le second a un changement de régime et constant par morceaux. La somme de ses deux sauts est nulle. Ainsi pour chacun de ces modèles nous avons étudié les propriétés asymptotiques de l’estimateur bayésien (EB) et celui du maximum de vraisemblance(EMV). Nous avons montré la consistance, la convergence en distribution et la convergence des moments. En particulier l’estimateur bayésien est asymptotiquement efficace. Pour le second modèle nous avons aussi considéré le test d’une hypothèse simple contre une alternative unilatérale et nous avons décrit les propriétés asymptotiques (choix du seuil et puissance ) du test de Wald (WT)et du test du rapport de vraisemblance généralisé (GRLT).Les démonstrations sont basées sur la méthode d’Ibragimov et Khasminskii. Cette dernière repose sur la convergence faible du rapport de vraisemblance normalisé dans l’espace de Skorohod sous certains critères de tension des familles demesure correspondantes.Par des simulations numériques, les variances limites nous ont permis de conclure que l’EB est meilleur que celui du EMV. Lorsque la somme des sauts est nulle, nous avons développé une approche numérique pour le EMV.Ensuite on a considéré le problème de construction d’un test d’ajustement pour un modèle avec un paramètre d’échelle. On a montré que dans ce cas, le test de Cramer-von Mises est asymptotiquement ”parameter-free” et est consistent. / This work is devoted to the parametric estimation, hypothesis testing and goodnessof-fit test problems for non homogenous Poisson processes. First we consider two models having two jumps located by an unknown parameter.For the first model the sum of jumps is positive. The second is a model of switching intensity, piecewise constant and the sum of jumps is zero. Thus, for each model, we studied the asymptotic properties of the Bayesian estimator (BE) andthe likelihood estimator (MLE). The consistency, the convergence in distribution and the convergence of moments are shown. In particular we show that the BE is asymptotically efficient. For the second model we also consider the problem of asimple hypothesis testing against a one- sided alternative. The asymptotic properties (choice of the threshold and power) of Wald test (WT) and the generalized likelihood ratio test (GRLT) are described.For the proofs we use the method of Ibragimov and Khasminskii. This method is based on the weak convergence of the normalized likelihood ratio in the Skorohod space under some tightness criterion of the corresponding families of measure.By numerical simulations, the limiting variances of estimators allows us to conclude that the BE outperforms the MLE. In the situation where the sum of jumps is zero, we developed a numerical approach to obtain the MLE.Then we consider the problem of construction of goodness-of-test for a model with scale parameter. We show that the Cram´er-von Mises type test is asymptotically parameter-free. It is also consistent.
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Tests d'ajustement pour des processus stochastiques dans le cas de l'hypothèse nulle paramétrique / On goodness-of-fit tests with parametric hypotheses for some stochastic processesBen Abdeddaiem, Maroua 11 May 2016 (has links)
Ce travail est consacré au problème de construction des tests d'ajustement dans le cas des processus stochastiques observés en temps continu. Comme modèles d'observations, nous considérons les processus de diffusion avec « petit bruit » et ergodique et le processus de Poisson non homogène. Sous l'hypothèse nulle, nous traitons le cas où chaque modèle dépend d'un paramètre inconnu unidimensionnel et nous proposons l'estimateur de distance minimale pour ce paramètre. Notre but est la construction des tests d'ajustement « asymptotically distribution free » (ADF) de niveau asymtotique α ϵ (0,1) dans le cas de cette hypothèse paramétrique pour les modèles traités. Nous montrons alors que la limite de chaque statistique étudiée ne dépend ni du modèle ni du paramètre inconnu. Les tests d'ajustement basés sur ces statistiques sont donc ADF. L'objectif principal de ce travail est la construction d'une transformation linéaire spéciale. En particulier, nous résolvons l'équation de Fredholm du second type avec le noyau dégénéré. Sa solution nous permet de construire la transformation linéaire désirée. Ensuite, nous montrons que l'application de cette transformation aux statistiques de base étudiées dans chaque modèle nous aide à introduire des statistiques ayant la même limite (l'intégrale du carrée du processus de Wiener). Cette dernière est « distribution free » vu qu'elle ne dépend ni du modèle ni du paramètre inconnu. Par conséquent, nous proposons des tests d'ajustement ADF en se basant sur cette transformation linéaire pour les processus de diffusion avec « petit bruit » et ergodique et le processus de Poisson non homogène. / This work is devoted to the problem of the construction of several goodness of-fit (GoF) tests in the case of somestochastic processes observed in continuous time. As models of observations, we take "small noise" and ergodic diffusionprocesses and an inhomogeneous Poisson process. Under the null hypothesis, we treat the case where each model depends on an unknown one-dimensional parameter and we consider the minimum distance estimator for this parameter. Our goal is to propose "asymptotically distribution free" (ADF) GoF tests of asymptotic size α ϵ (0,1) in the case of the parametric null hypotheses for the considered models. Indeed, we show that the limit of each studied statistic does not depend on the model and the unknown parameter. Therefore, the tests based on these statistics are ADF.The main purpose of this work is to construct a special linear transformation. In particular, we solve Fredholm equation ofthe second kind with degenerated kernel. Its solution gives us the desired linear transformation. Next, we show that theapplication of this transformation to the basic statistics allows us to introduce statistics with the same limit (the integral of the square of the Wiener process). The latter is "distribution free" because it does not depend on the models and the unknown parameter. Therefore, we construct the ADF GoF tests which are based on this linear transformation for the diffusion ("small noise" and ergodic) and inhomogeneous Poisson processes.
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A CUSUM test for discrete monitoring of intensity of a Poisson processEger, Karl-Heinz 13 June 2010 (has links)
This paper deals with CUSUM tests for monitoring
of intensity parameter of a Poisson process if this
process can be observed in a restricted manner only at pregiven
equidistant time points. In this case the process can
be monitored by means of a CUSUM test for the parameter
of a corresponding Poisson distribution.
For rational reference parameter values the computation
of average run length is reduced to that of solving of a
system of simultaneous linear equations. The performance
of obtained CUSUM tests is discussed by means of corresponding
examples.
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Performance modeling of congestion control and resource allocation under heterogeneous network traffic. Modeling and analysis of active queue management mechanism in the presence of poisson and bursty traffic arrival processes.Wang, Lan January 2010 (has links)
Along with playing an ever-increasing role in the integration of other communication networks and expanding in application diversities, the current Internet suffers from serious overuse and congestion bottlenecks. Efficient congestion control is fundamental to ensure the Internet reliability, satisfy the specified Quality-of-Service (QoS) constraints and achieve desirable performance in response to varying application scenarios. Active Queue Management (AQM) is a promising scheme to support end-to-end Transmission Control Protocol (TCP) congestion control because it enables the sender to react appropriately to the real network situation. Analytical performance models are powerful tools which can be adopted to investigate optimal setting of AQM parameters. Among the existing research efforts in this field, however, there is a current lack of analytical models that can be viewed as a cost-effective performance evaluation tool for AQM in the presence of heterogeneous traffic, generated by various network applications.
This thesis aims to provide a generic and extensible analytical framework for analyzing AQM congestion control for various traffic types, such as non-bursty Poisson and bursty Markov-Modulated Poisson Process (MMPP) traffic. Specifically, the Markov analytical models are developed for AQM congestion control scheme coupled with queue thresholds and then are adopted to derive expressions for important QoS metrics. The main contributions of this thesis are listed as follows:
iii
¿ Study the queueing systems for modeling AQM scheme subject to single-class and multiple-classes Poisson traffic, respectively. Analyze the effects of the varying threshold, mean traffic arrival rate, service rate and buffer capacity on the key performance metrics.
¿ Propose an analytical model for AQM scheme with single class bursty traffic and investigate how burstiness and correlations affect the performance metrics. The analytical results reveal that high burstiness and correlation can result in significant degradation of AQM performance, such as increased queueing delay and packet loss probability, and reduced throughput and utlization.
¿ Develop an analytical model for a single server queueing system with AQM in the presence of heterogeneous traffic and evaluate the aggregate and marginal performance subject to different threshold values, burstiness degree and correlation.
¿ Conduct stochastic analysis of a single-server system with single-queue and multiple-queues, respectively, for AQM scheme in the presence of multiple priority traffic classes scheduled by the Priority Resume (PR) policy.
¿ Carry out the performance comparison of AQM with PR and First-In First-Out (FIFO) scheme and compare the performance of AQM with single PR priority queue and multiple priority queues, respectively.
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