Global ETD Search

121	Abschätzungen der Konvergenzgeschwindigkeit im zentralen Grenzwertsatz Paditz, Ludwig January 1976 (has links) Der Beitrag stellt eine Verallgemeinerung der Ergebnisse dar, die in den Informationen/07; 1976,05 veröffentlicht wurden. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und nicht notwendig identisch verteilte Zufallsgrößen mit endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_m derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsatz explizit angeben können. Als Spezialfall ergibt sich die ungleichmäßige Fehlerschranke von A.BIKELIS (1966) im Fall der Existenz dritter absoluter Momente. Weiterhin werden Grenzwertsätze unter Voraussetzung einseitiger Momente betrachtet. Es werden einige Literaturhinweise angegeben.:1. Grenzwertsätze für verschieden verteilte Zufallsgrößen S. 1 2. Grenzwertsätze unter Voraussetzung einseitiger Momente S. 6 3. Beweise zum Abschnitt 1 S. 7 4. Beweise zum Abschnitt 2 S. 14 Literatur S. 16 / The paper is a generalization of the results, published by the author in Informationen/07; 1976,05. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are non iid random variables with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_m are computed such that we have some error estimates in the nonuniform central limit theorem. A special case is the nonuniform error bound by A.BIKELIS (1966) in the case of existence of third absolute moments. Furthermore limit theorems with assumption of onesided moments are considered. Some references are given.:1. Grenzwertsätze für verschieden verteilte Zufallsgrößen S. 1 2. Grenzwertsätze unter Voraussetzung einseitiger Momente S. 6 3. Beweise zum Abschnitt 1 S. 7 4. Beweise zum Abschnitt 2 S. 14 Literatur S. 16 info:eu-repo/classification/ddc/510 ddc:510
122	Über eine Fehlerabschätzung im zentralen Grenzwertsatz Paditz, Ludwig January 1979 (has links) Es wird eine Folge unabhängiger zentrierter Zufallsgrößen betrachtet, die absolute Momente der Ordnung m, 2<m<3, besitzen mögen. Dann gelten für die normierte Verteilungsfunktion der Zufallssumme X_1+X_2+...+X_n der zentrale Grenzwertsatz und insbesondere eine ungleichmäßige Fehlerabschätzung von A.BIKELIS (1966). In der vorliegenden Note werden die analytische Struktur der in dieser Fehlerabschätzung auftretenden Konstanten L=L(m) genauer untersucht sowie dazu erzielte numerische Resultate vorgelegt. Abschließend werden einige Literaturhinweise angegeben. Der Fall m=3 wurde bereits in der Dissertation (TU Dresden 1977) des Autors untersucht. / We consider a sequence of centered and independent random variables with moments of order m, 2<m<3. Now the central limit theorem for the distribution function of the normed sum X_1+X_2+...+X_n and especially a nonuniform error estimate by A.BIKELIS (1966) hold. In this paper the analytical structure of the appearing constant L=L(m) of the error bound and numerical results are presented. Finally some references are given. The case m=3 was already studied in the thesis (Dissertation TU Dresden, 1977) by the author. info:eu-repo/classification/ddc/510 ddc:510
123	Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz Paditz, Ludwig 04 June 2013 (has links) (PDF) In der Arbeit wird das asymptotische Verhalten von geeignet normierten und zentrierten Summen von Zufallsgrößen untersucht, die entweder unabhängig sind oder im Falle der Abhängigkeit als Martingaldifferenzfolge oder stark multiplikatives System auftreten. Neben der klassischen Summationstheorie werden die Limitierungsverfahren mit einer unendlichen Summationsmatrix oder einer angepaßten Folge von Gewichtsfunktionen betrachtet. Es werden die Methode der charakteristischen Funktionen und besonders die direkte Methode der konjugierten Verteilungsfunktionen weiterentwickelt, um quantitative Aussagen über gleichmäßige und ungleichmäßige Restgliedabschätzungen in zentralen Grenzwertsatz zu beweisen. Die Untersuchungen werden dabei in der Lp-Metrik, 1<p<oo oder p=1 bzw. p=oo, durchgeführt, wobei der Fall p=oo der üblichen sup-Norm entspricht. Darüber hinaus wird im Fall unabhängiger Zufallsgrößen der lokale Grenzwertsatz für Dichten betrachtet. Mittels der elektronischen Datenverarbeitung neue numerische Resultate zu erhalten. Die Arbeit wird abgerundet durch verschiedene Hinweise auf praktische Anwendungen. / In the work the asymptotic behavior of suitably centered and normalized sums of random variables is investigated, which are either independent or occur in the case of dependence as a sequence of martingale differences or a strongly multiplicative system. In addition to the classical theory of summation limiting processes are considered with an infinite summation matrix or an adapted sequence of weighting functions. It will be further developed the method of characteristic functions, and especially the direct method of the conjugate distribution functions to prove quantitative statements about uniform and non-uniform error estimates of the remainder term in central limit theorem. The investigations are realized in the Lp metric, 1 <p <oo or p = 1 or p = oo, where in the case p = oo it is the usual sup-norm. In addition, in the case of independent random variables the local limit theorem for densities is considered. By means of electronic data processing new numerical results are obtained. The work is finished by various references to practical applications. Zentraler Grenzwertsatz Summen unabhängiger Zufallsgrößen Doppelfolge von Zufallssgrößen Martingaldifferenzfolgen stark multiplikative Systeme Zufallsvektoren Zufallselemente Verteilungsfunktion Dichtefunktion charakteristische Funktionen konjugierte Verteilungen zufälliger Index Konvergenzgeschwindigkeit ungleichmäßige Fehlerabschätzung einseitige Momente Pseudomomente abgeschnittene Momente Limitierungsverfahren Lp-Metrik globaler zentraler Grenzwertsatz Ordnung der Konvergenzgeschwindigkeit Fehlerabschätzung mittlere Abweichungen central limit theorem sums of independent random variables triangular arrays of random variables series of independent random variables sequences of martingale differences strongly multiplicative systems random vectors random elements distribution function density function characteristic functions conjugate distributions random index speed of convergence nonuniform error estimate one-sided moments pseudo moments truncated moments limiting methods Lp-metric global central limit theorem nonuniform central limit theorem order of the speed of convergence error estimation moderate deviations ddc:510 rvk:SK 800
124	Beiträge zur expliziten Fehlerabschätzung im zentralen Grenzwertsatz Paditz, Ludwig 27 April 1989 (has links) In der Arbeit wird das asymptotische Verhalten von geeignet normierten und zentrierten Summen von Zufallsgrößen untersucht, die entweder unabhängig sind oder im Falle der Abhängigkeit als Martingaldifferenzfolge oder stark multiplikatives System auftreten. Neben der klassischen Summationstheorie werden die Limitierungsverfahren mit einer unendlichen Summationsmatrix oder einer angepaßten Folge von Gewichtsfunktionen betrachtet. Es werden die Methode der charakteristischen Funktionen und besonders die direkte Methode der konjugierten Verteilungsfunktionen weiterentwickelt, um quantitative Aussagen über gleichmäßige und ungleichmäßige Restgliedabschätzungen in zentralen Grenzwertsatz zu beweisen. Die Untersuchungen werden dabei in der Lp-Metrik, 1<p<oo oder p=1 bzw. p=oo, durchgeführt, wobei der Fall p=oo der üblichen sup-Norm entspricht. Darüber hinaus wird im Fall unabhängiger Zufallsgrößen der lokale Grenzwertsatz für Dichten betrachtet. Mittels der elektronischen Datenverarbeitung neue numerische Resultate zu erhalten. Die Arbeit wird abgerundet durch verschiedene Hinweise auf praktische Anwendungen. / In the work the asymptotic behavior of suitably centered and normalized sums of random variables is investigated, which are either independent or occur in the case of dependence as a sequence of martingale differences or a strongly multiplicative system. In addition to the classical theory of summation limiting processes are considered with an infinite summation matrix or an adapted sequence of weighting functions. It will be further developed the method of characteristic functions, and especially the direct method of the conjugate distribution functions to prove quantitative statements about uniform and non-uniform error estimates of the remainder term in central limit theorem. The investigations are realized in the Lp metric, 1 <p <oo or p = 1 or p = oo, where in the case p = oo it is the usual sup-norm. In addition, in the case of independent random variables the local limit theorem for densities is considered. By means of electronic data processing new numerical results are obtained. The work is finished by various references to practical applications. info:eu-repo/classification/ddc/510 ddc:510
125	Satisticing solutions for multiobjective stochastic linear programming problems Adeyefa, Segun Adeyemi 06 1900 (has links) Multiobjective Stochastic Linear Programming is a relevant topic. As a matter of fact, many real life problems ranging from portfolio selection to water resource management may be cast into this framework. There are severe limitations in objectivity in this field due to the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice does not hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this thesis, we resort to the bounded rationality and chance-constrained principles to define satisficing solutions for Multiobjective Stochastic Linear Programming problems. These solutions are then characterized for the cases of normal, exponential, chi-squared and gamma distributions. Ways for singling out such solutions are discussed and numerical examples provided for the sake of illustration. Extension to the case of fuzzy random coefficients is also carried out. / Decision Sciences Multiobjective programming Stochastic programming Linear programming Satisfying solution Chance constrained Expected value optimality/efficiency Variance optimality/efficiency Minimum risk optimality/efficiency Fuzzy random variables Random closed sets Embedding theorem 519.72 Linear programming Stochastic processes
126	Value at risk et expected shortfall pour des données faiblement dépendantes : estimations non-paramétriques et théorèmes de convergences / Value at risk and expected shortfall for weak dependent random variables : nonparametric estimations and limit theorems Kabui, Ali 19 September 2012 (has links) Quantifier et mesurer le risque dans un environnement partiellement ou totalement incertain est probablement l'un des enjeux majeurs de la recherche appliquée en mathématiques financières. Cela concerne l'économie, la finance, mais d'autres domaines comme la santé via les assurances par exemple. L'une des difficultés fondamentales de ce processus de gestion des risques est de modéliser les actifs sous-jacents, puis d'approcher le risque à partir des observations ou des simulations. Comme dans ce domaine, l'aléa ou l'incertitude joue un rôle fondamental dans l'évolution des actifs, le recours aux processus stochastiques et aux méthodes statistiques devient crucial. Dans la pratique l'approche paramétrique est largement utilisée. Elle consiste à choisir le modèle dans une famille paramétrique, de quantifier le risque en fonction des paramètres, et d'estimer le risque en remplaçant les paramètres par leurs estimations. Cette approche présente un risque majeur, celui de mal spécifier le modèle, et donc de sous-estimer ou sur-estimer le risque. Partant de ce constat et dans une perspective de minimiser le risque de modèle, nous avons choisi d'aborder la question de la quantification du risque avec une approche non-paramétrique qui s'applique à des modèles aussi généraux que possible. Nous nous sommes concentrés sur deux mesures de risque largement utilisées dans la pratique et qui sont parfois imposées par les réglementations nationales ou internationales. Il s'agit de la Value at Risk (VaR) qui quantifie le niveau de perte maximum avec un niveau de confiance élevé (95% ou 99%). La seconde mesure est l'Expected Shortfall (ES) qui nous renseigne sur la perte moyenne au delà de la VaR. / To quantify and measure the risk in an environment partially or completely uncertain is probably one of the major issues of the applied research in financial mathematics. That relates to the economy, finance, but many other fields like health via the insurances for example. One of the fundamental difficulties of this process of management of risks is to model the under lying credits, then approach the risk from observations or simulations. As in this field, the risk or uncertainty plays a fundamental role in the evolution of the credits; the recourse to the stochastic processes and with the statistical methods becomes crucial. In practice the parametric approach is largely used.It consists in choosing the model in a parametric family, to quantify the risk according to the parameters, and to estimate its risk by replacing the parameters by their estimates. This approach presents a main risk, that badly to specify the model, and thus to underestimate or over-estimate the risk. Based within and with a view to minimizing the risk model, we choose to tackle the question of the quantification of the risk with a nonparametric approach which applies to models as general as possible. We concentrate to two measures of risk largely used in practice and which are sometimes imposed by the national or international regulations. They are the Value at Risk (VaR) which quantifies the maximum level of loss with a high degree of confidence (95% or 99%). The second measure is the Expected Shortfall (ES) which informs about the average loss beyond the VaR. Value at Risk (VaR) Expected Shortfall (ES) Représentation de Bahadur Fonction de quantile Processus empirique Module de continuité Normalité asymptotique Estimation non-paramétrique Inégalité de moment Variables faiblement dépendantes Value at Risk (VaR) Expected Shortfall (ES) Bahadur representation Quantile function Empirical process Modulus of continuity Asymptotic normality Nonparametric estimation Moment’s inequality Weak dependent random variables
127	Gráfico de controle para monitoramento da razão da demanda e mão de obra em retaguarda de serviços no setor bancário. / A control chart to monitor the ratio of demand and manpower in a backoffice service in a business banking. Hiratsuca, Simone 26 April 2016 (has links) O monitoramento da razão Z de duas variáveis através de gráfico de controle tem sido um tema recentemente explorado na literatura. Para analisar mais o assunto, o estudo avalia a eficiência e viabilidade de aplicação dessa ferramenta como suporte na tomada de decisão para gerenciamento de capacidade de mão de obra de retaguarda (doravante mencionado como Backoffice) de serviço de empresa do setor bancário. Tradicionalmente, gráficos de controle tem sido utilizados para monitorar o processo produtivo de manufaturas, mas recentemente tem sido adotado para monitoramento de alguns serviços. Apesar de ainda seguir muitos conceitos pioneiros na manufatura, a atividade do setor de serviços apresenta suas particularidades como, por exemplo, a impossibilidade de gerar estoque. Assim, a necessidade de adequar seus recursos à demanda torna-se essencial, sendo fundamental a gestão de controles e sua urgência para que possa reagir rapidamente em caso de variação de demanda e adequar sua capacidade. Em um cenário de restrição de recursos, planejar é crucial para evitar desperdícios e garantir eficiência. O objetivo deste estudo é apresentar o gráfico de controle como ferramenta para monitorar a razão de duas variáveis aleatórias: a demanda e a mão de obra em Backoffice de serviço em um banco. Nesse trabalho, gráfico de controle de Shewhart tradicional e gráfico de controle de Shewhart com regras suplementares são analisados e os resultados obtidos confirmam a possibilidade de utilização da ferramenta de gráficos de controle para o gerenciamento e adequação de mão de obra para atender a demanda. O monitoramento da razão (demanda/ mão de obra) ajudará o gestor a alocar adequadamente o time (mão de obra) de acordo com a demanda e a capacidade produtiva. Como contribuição, o estudo avalia o comportamento da razão Z = X/Y em situação de alta variabilidade da variável X e baixa variabilidade da variável Y . / The monitoring of the ratio Z of two variables through control chart has been recently explored in the literature. This study analyses the efficiency and viability of this tool as a support to the manager\'s decision in capacity management of a Backoffice service in a business banking service. Traditionally, control charts have been used to monitoring production process in manufacturing companies, but recently it has been adopted in monitoring some classes of services. Although many pioneering definitions developed for manufacturing are still applied in the service activities, the service industry has some particularities as the impossibility to generate stock, for example. Thus, the need to adapt the resources of manpower to attend the demand becomes essential mainly in a current financial global crisis, with resource constraints. The control management is fundamental and urgent to plan a fast reaction to adequate its capacity in case of a large demand variation. Thus, monitoring is crucial to avoid vast and ensure efficiency. The aim of this paper is to present a control chart to monitor the ratio of the two random quantities: the demand and the labor of a Backoffice service in a business banking service. In this paper, traditional Shewhart and Shewhart with supplementary rules control charts are considered and the results confirmed the possibility to apply the control charts to help the management to adequate the manpower in order to attend the demand. The monitoring of the ratio (demand/manpower) will help the manager to allocate adequately the team (the manpower) according to the demand and the production capacity. The contribution of this study is the analysis of the behavior of the ratio Z = X/Y in situation of large variability of the variable X and low variability of the variable Y . Control chart in resources management Demanda Gráficos Index resource and demand management Manpower management in service Mão-de-obra (Controle; Gerenciamento) Ratio of normal random variables Razão de variáveis normais Regras suplementares Supplementary rules
128	模糊隨機變數在線性迴歸模式上的應用 / Fuzzy Random Variables and Its Applications in Fuzzy Regression Model 曾能芳 Unknown Date (has links) 傳統迴歸分析是假設觀測值的不確定性來自於隨機現象，本文則應用模糊隨機變數概念於迴歸模式的架構，考慮將隨機現象和模糊認知並列研究。針對樣本模糊數(x<sub>i</sub>, Y<sub>i</sub>)，我們進行模糊迴歸參數估計，並稱此為模糊迴歸模式分析。模糊迴歸參數估計大都採用線性規劃，求出適當區間，將觀測模糊數Y<sub>i</sub>的分佈範圍全部覆蓋。但是此結果並不能充分反映觀測樣本Y<sub>i</sub>的特性。本研究提出一套模糊迴歸參數的估計方法，其結果對觀測樣本的解釋將更為合理，且具有模糊不偏的特性。在分析過程中，我們亦提出一些模糊統計量如模糊期望值、模糊變異數、模糊中位數的定義，以增加對這些參數的模糊理解。最後在本文中也針對台灣景氣指標與經濟成長率作實務分析，說明模糊迴歸模式的適用性。 / Conventional study on the regression analysis is based on the conception that the uncertainty of observed data comes from the random property. However, in this paper we consider both of the random property and the fuzzy perception to construct the regression model by using of fuzzy random variables. For the fuzzy sample (x<sub>i</sub>,Y<sub>i</sub>), we will process the parameters estimation of the fuzzy regression, and we call this process as fuzzy regression analysis. The parameters estimation for a fuzzy regression model is generally derived by the linear programming scheme. But it's result usually doesn't sufficiently reflect the characteristics of the observed samples. Hence in this paper we propose an alternative technique for parameters estimation in constructing the fuzzy regression model. The result will describe the observed data better than the conventional method did, moreover it will have the fuzzy unbiased properties. For the purpose of fuzzy perception on the fuzzy random variables, we also give definitions for certain important fuzzy statistics such as fuzzy expected value, fuzzy variance and fuzzy median. Finally, we give an example about the Taiwan Business Cycle and the Taiwan Economic Growth Rate for illustration. 集合表徵模糊隨機變數模糊迴歸模式模糊期望值模糊分配函數模糊不偏性 set representation fuzzy random variables fuzzy regression model fuzzy expected value fuzzy distribution function fuzzy unbiased
129	Επίδοση συστημάτων διαφορισμού MIMO σε γενικευμένα κανάλια διαλείψεων / Performance analysis of MIMO diversity systems over generalized fading channels Ροπόκης, Γεώργιος 21 March 2011 (has links) Στο πλαίσιο αυτής της διατριβής μελετάται η επίδοση συστημάτων διαφορισμού MIMO σε γενικευμένα κανάλια διαλείψεων. Αρχικά, εξετάζεται η επίδοση των OSTBC σε περιβάλλοντα διαλείψεων Hoyt. Αποδεικνύεται ότι, στην περίπτωση τέτοιων συστημάτων, ο σηματοθορυβικός λόγος (signal to noise ratio, SNR) εκφράζεται ως μία τετραγωνική μορφή κανονικών τυχαίων μεταβλητών και γίνεται χρήση της συνάρτησης πυκνότητας πιθανότητας και της αθροιστικής συνάρτησης κατανομής αυτής της μορφής για τον υπολογισμό των μετρικών επίδοσης. Επιπλέον, μελετάται η σύγκλιση των σειρών που χρησιμοποιούνται για τον υπολογισμό των δύο αυτών συναρτήσεων και κατασκευάζονται νέα άνω φράγματα για το σφάλμα αποκοπής των σειρών. Τα φράγματα αυτά είναι σαφώς πιο αυστηρά από τα ήδη γνωστά από τη βιβλιογραφία. Στη συνέχεια, εισάγεται ένα γενικευμένο μοντέλο διαλείψεων για την ανάλυση επίδοσης των OSTBC και των δεκτών MRC και υπολογίζονται όλες οι μετρικές επίδοσης των δύο συστημάτων για το συγκεκριμένο μοντέλο διαλείψεων. Το μοντέλο αυτό περιλαμβάνει ως ειδικές περιπτώσεις τα πλέον διαδεδομένα μοντέλα καναλιών διαλείψεων, ενώ επιπλέον, επιτρέπει την ανάλυση επίδοσης σε μικτά περιβάλλοντα διαλείψεων όπου τα πολλαπλά κανάλια μπορούν να ακολουθούν διαφορετικές κατανομές. Στη συνέχεια, μελετάται η επίδοση συστημάτων συνεργατικού διαφορισμού με χρήση αναμεταδοτών ανίχνευσης και προώθησης (Detect and Forward, DaF) σε περιβάλλοντα διαλείψεων Rayleigh. Εξετάζονται τρεις διαφορετικοί δέκτες και υπολογίζεται η πιθανότητα σφάλματος ανά bit γι' αυτούς. Τέλος προτείνεται ένας νέος δέκτης για συνεργατικά συστήματα DaF και αποδεικνύεται η ανωτερότητά του σε σύγκριση με τους υπόλοιπους μελετώμενους δέκτες. Όλα τα θεωρητικά αποτελέσματα που παρουσιάζονται στο πλαίσιο της διατριβής συγκρίνονται με αποτελέσματα προσομοιώσεων Monte Carlo που αποδεικνύουν την ορθότητα της ανάλυσης. / This thesis studies the performance of MIMO diversity systems in generalized fading channels. First, we examine the performance of OSTBC in Hoyt fading channels. It is proven that, for this fading model, and when an OSTBC is employed, the signal-to-noise ratio (SNR) of the OSTBC can be expressed as a quadratic form in normal random variables. Therefore, the performance analysis for OSTBC over Hoyt fading channels is performed using the PDF and the CDF of such quadratic forms. In the statistical literature, these functions are expressed in terms of infinite series. The convergence of the series is thoroughly studied and new expressions for the truncation error bound of these series are proposed. The proposed bounds are much tighter than the bounds that can be found in the literature. The expressions for the PDF and the CDF are then used for the performance analysis of OSTBC over Hoyt fading and several performance metrics are calculated. Then, a generalized fading model for the performance analysis of OSTBC and MRC is proposed and the theoretical performance analysis of both MRC and OSTBC is carried out. The main advantage of this model is the fact that it includes as special cases most of the widely used fading models. Furthermore, the performance of cooperative diversity systems employing Detect and Forward (DaF) relays is studied for Rayleigh fading channels. More specifically, three low complexity detection algorithms for these channels are examined and closed-form expressions of the bit error probability (BEP) for these receivers are derived. Finally, a new low complexity receiver for cooperative systems with DaF relays is proposed. Using Monte Carlo Simulations it is shown that this receiver outperforms the three receivers that have been studied. For the systems studied in the thesis, the performance analysis results that have been derived theoretically are compared with Monte Carlo simulations that prove the validity of the analysis. Κανάλια διαλείψεων Τεχνικές διαφορισμού 384.5 Wireless communications Fading channels Multiple-input multiple-output systems Orthogonal space time block codes Diversity techniques Cooperative diversity techniques
130	Estimation de paramètres en exploitant les aspects calculatoires et numériques Kadje Kenmogne, Romain 08 1900 (has links) No description available. Convergence de variables aléatoires Copule Différence de variables de loi gamma Estimateur équivariant Estimation des paramètres Fonction caractéristique Méthode bayésienne Pseudo-vraisemblance Rapport de variables gaussiennes Vraisemblance des rangs Bayesian method Characteristic function Convergence of random variables Copula Difference of gamma variates Equivariant estimator Parameter estimation Pseudo-likelihood Rank-likelihood Ratio of normal variables

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