Relevant bibliographies by topics / Distributions stables

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Academic literature on the topic 'Distributions stables'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Distributions stables"

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Zydor, Michał. "La Variante infinitésimale de la formule des traces de Jacquet-Rallis pour les groupes unitaires." Canadian Journal of Mathematics 68, no. 6 (December 1, 2016): 1382–435. http://dx.doi.org/10.4153/cjm-2015-054-9.

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RésuméNous établissons une variante infinitésimale de la formule des traces de Jacquet-Rallis pour les groupes unitaires. Notre formule s’obtient par intégration d'un noyau tronqué á la Arthur. Elle posséde un côté géométrique qui est une somme de distributions Jo indexée par les classes d'éléments de l'ébre de Lie de U(n + 1) stables par U(n)-conjugaison ainsi qu'un “côté spectral” formé des transformées de Fourier des distributions précédentes. On démontre que les distributions Jo sont invariantes et ne dépendent que du choix de lamesure deHaar sur U(n)(𝔸). Pour des classes o semi-simples réguliéres, Jo est une intégrale orbitale relative de Jacquet-Rallis. Pour les classes o dites relativement semi-simples régulières, on exprime Jo en terme des intégrales orbitales relatives régularisées á l'aide des fonctions zêta.
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Guevara, Cira, and Thiago R. Sousa. "ESTIMADOR SIMPLE Y FUERTEMENTE CONSISTENTE DE DISTRIBUCIONES ESTABLES." Selecciones Matemáticas 3, no. 1 (June 30, 2016): 25–31. http://dx.doi.org/10.17268/sel.mat.2016.01.04.

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Nguyen, T. T. "Conditional Distributions and Characterizations of Multivariate Stable Distribution." Journal of Multivariate Analysis 53, no. 2 (May 1995): 181–93. http://dx.doi.org/10.1006/jmva.1995.1031.

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Panton, Don B. "Cumulative distribution function values for symmetric standardized stable distributions." Communications in Statistics - Simulation and Computation 21, no. 2 (1992): 485–92. http://dx.doi.org/10.1080/03610919208813030.

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Ejsmont, Wiktor. "A Characterization of Symmetric Stable Distributions." Journal of Function Spaces 2016 (2016): 1–3. http://dx.doi.org/10.1155/2016/8384767.

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Characterization problems in probability are studied here. Using the characteristic function of an additive convolution we generalize some known characterizations of the normal distribution to stable distributions. More precisely, if a distribution of a linear form depends only on the sum of powers of the certain parameters, then we obtain symmetric stable distributions.
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Саенко, В. В., and V. V. Saenko. "Дробно-устойчивая статистика экспрессии генов в экспериментальных данных секвенирования нового поколения." Mathematical Biology and Bioinformatics 11, no. 2 (November 25, 2016): 278–87. http://dx.doi.org/10.17537/2016.11.278.

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As has been shown, in the author's published articles, that the application of class of the fractional-stable laws to the genes expression results obtained by DNA-microarys leads to poor agreement between experimental and theoretical distributions. This difference can be explained by the imperfection of the technology of the gene expression determination. In this article the distributions of the gene expression obtained by Next Generation Sequence technology are investigated. In this technology the determination technique of the gene expression differs from the DNA-microarrays technology. This results to more qualitative results of an approximation. In particular, it is established that the probability density function of the gene expression has a form of shift-scale mixture of probability laws, where one of the components of the mixture is the fractional-stable distribution.
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Ravi, S., and TS Mavitha. "THE INTERPLAY BETWEEN I-MAX, I-MIN, P-MAX AND P-MIN STABLE DISTRIBUTIONS." Mathematical Journal of Interdisciplinary Sciences 4, no. 1 (September 1, 2015): 49–53. http://dx.doi.org/10.15415/mjis.2015.41006.

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Khokhlov, Yury, Victor Korolev, and Alexander Zeifman. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems." Mathematics 8, no. 5 (May 8, 2020): 749. http://dx.doi.org/10.3390/math8050749.

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In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate stable distributions. Multivariate analogs of the Mittag–Leffler distribution are introduced. Some properties of these distributions are discussed. The main focus is on the representations of the corresponding random vectors as products of independent random variables and vectors. In these products, relations are traced of the distributions of the involved terms with popular probability distributions. As examples of distributions of the class of scale mixtures of multivariate stable distributions, multivariate generalized Linnik distributions and multivariate generalized Mittag–Leffler distributions are considered in detail. Their relations with multivariate ‘ordinary’ Linnik distributions, multivariate normal, stable and Laplace laws as well as with univariate Mittag–Leffler and generalized Mittag–Leffler distributions are discussed. Limit theorems are proved presenting necessary and sufficient conditions for the convergence of the distributions of random sequences with independent random indices (including sums of a random number of random vectors and multivariate statistics constructed from samples with random sizes) to scale mixtures of multivariate elliptically contoured stable distributions. The property of scale-mixed multivariate elliptically contoured stable distributions to be both scale mixtures of a non-trivial multivariate stable distribution and a normal scale mixture is used to obtain necessary and sufficient conditions for the convergence of the distributions of random sums of random vectors with covariance matrices to the multivariate generalized Linnik distribution.
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Song, Guan, An Na, Liu Jinhua, Zong Ning, He Yongtao, Shi Peili, Zhang Jinjing, and He Nianpeng. "Warming impacts on carbon, nitrogen and phosphorus distribution in soil water-stable aggregates." Plant, Soil and Environment 64, No. 2 (February 6, 2018): 64–69. http://dx.doi.org/10.17221/715/2017-pse.

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A five-year (2010–2015) field experiment was conducted to investigate warming impacts on organic carbon (OC), total nitrogen (TN) and total phosphorus (TP) contents and their ratios in bulk soil and soil water-stable aggregates in an alpine meadow of the Tibetan Plateau. Compared with unwarmed control, warming had no significant effects on OC, TN and TP contents and their ratios in bulk soil. The contents of OC, TN and TP associated with macroaggregates and microaggregates decreased, whereas those associated with silt + clay fractions significantly increased. The C:N and C:P ratios in macro- and microaggregates and silt + clay fractions decreased, with significant differences for C:P ratio in microaggregates and C:N and C:P ratios in silt + clay fractions. The results indicated that C, N and P were protected chemically in silt- and clay-size fractions under warming, which offset the loss of C, N and P protected physically by macro- and microaggregates. Both physically and chemically protected C decomposition proceeded relatively more rapidly or accumulated relatively more slowly than did N and P. Our results suggest that C, N and P distributions within soil aggregate size fractions influence their net changes in bulk soil under future climate change scenarios.
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Nagaev, A. V., and S. M. Shkol’nik. "Some Properties of Symmetric Stable Distributions Close to the Normal Distribution." Theory of Probability & Its Applications 33, no. 1 (January 1989): 139–44. http://dx.doi.org/10.1137/1133014.

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Dissertations / Theses on the topic "Distributions stables"

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Wang, Min. "Generalized stable distributions and free stable distributions." Thesis, Lille 1, 2019. http://www.theses.fr/2019LIL1I032/document.

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Cette thèse porte sur les lois stables réelles au sens large et comprend deux parties indépendantes. La première partie concerne les lois stables généralisées introduites par Schneider dans un contexte physique et étudiées ensuite par Pakes. Elles sont définies par une équation différentielle fractionnaire dont on caractérise ici l'existence et l'unicité des solutions densité à l'aide de deux paramètres positifs, l'un de stabilité et l'autre de biais. On montre ensuite diverses identités en loi pour les variables aléatoires sous-jacentes. On étudie le comportement asymptotique précis de la densité aux deux extrémités du support. Dans certains cas, on donne des représentations exactes de ces densités comme fonctions de Fox. Enfin, on résout entièrement les questions ouvertes autour de l'infinie divisibilité des lois stables généralisées. La seconde partie, plus longue, porte sur l'analyse classique des lois alpha-stables libres réelles. Introduites par Bercovici et Pata, ces lois ont ensuite étudiées par Biane, Demni et Hasebe-Kuznetsov sous divers points de vue. Nous montrons qu'elles sont classiquement infiniment divisibles pour alpha inférieur ou égal à 1 et qu'elles appartiennent à la classe de Thorin étendue pour alpha inférieur ou égal à 3/4. La mesure de Lévy est calculée explicitement pour alpha = 1 et ce calcul entraîne que les lois 1-stables libres n'appartiennent pas à la classe de Thorin, sauf dans le cas de la loi de Cauchy avec dérive. Dans le cas symétrique, nous montrons que les densités alpha-stables libres ne sont pas infiniment divisibles quand alpha supérieur à 1. Dans le cas de signe constant nous montrons que les densités stables libres ont une courbe en baleine, autrement dit que leurs dérivées successives ne s'annulent qu'une seule fois sur leurs supports, ce qui constitue un raffinement de l'unimodalité et fait écho à la courbe en cloche des densités stables classiques récemment montrée rigoureusement. Nous établissons enfin plusieurs propriétés précises des densités stables libres spectralement de signe constant, parmi lesquelles une analyse détaillée de la variable aléatoire de Kanter, des expansions asymptotiques complètes en zéro, ainsi que plusieurs propriétés intrinsèques des courbes en baleine. Nous montrons enfin une nouvelle identité en loi pour l'algèbre Beta-Gamma, diverses propriétés d'ordre stochastique et nous étudions le problème classique de Van Dantzig pour la loi semi-circulaire généralisée
This thesis deals with real stable laws in the broad sense and consists of two independent parts. The first part concerns the generalized stable laws introduced by Schneider in a physical context and then studied by Pakes. They are defined by a fractional differential equation, whose existence and uniqueness of the density solutions is here characterized via two positive parameters, a stability parameter and a bias parameter. We then show various identities in law for the underlying random variables. The precise asymptotic behaviour of the density at both ends of the support is investigated. In some cases, exact representations as Fox functions of these densities are given. Finally, we solve entirely the open questions on the infinite divisibility of the generalized stable laws. The second and longer part deals with the classical analysis of the free alpha-stable laws. Introduced by Bercovici and Pata, these laws were then studied by Biane, Demni and Hasebe-Kuznetsov, from various points of view. We show that they are classically infinitely divisible for alpha less than or equal to 1 and that they belong to the extended Thorin class extended for alpha less than or equal to 3/4. The Lévy measure is explicitly computed for alpha = 1, showing that free 1-stable distributions are not in the Thorin class except in the drifted Cauchy case. In the symmetric case we show that the free alpha-stable densities are not infinitely divisible when alpha larger than 1. In the one-sided case we prove, refining unimodality, that the densities are whale-shaped, that is their successive derivatives vanish exactly once on their support. This echoes the bell shape property of the classical stable densities recently rigorously shown. We also derive several fine properties of spectrally one-sided free stable densities, including a detailed analysis of the Kanter random variable, complete asymptotic expansions at zero, and several intrinsic features of whale-shaped functions. Finally, we display a new identity in law for the Beta-Gamma algebra, various stochastic order properties, and we study the classical Van Danzig problem for the generalized semi-circular law
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Ben, Maad Hassen. "Optimisation des stratégies de décodage des codes LDPC dans les environnements impulsifs : application aux réseaux de capteurs et ad hoc." Thesis, Reims, 2011. http://www.theses.fr/2011REIMS023/document.

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L’objectif de cette thèse est d’étudier le comportement des codes LDPC dans un environnement où l’interférence générée par un réseau n’est pas de nature gaussienne mais présente un caractère impulsif. Un premier constat rapide montre que sans précaution, les performances de ces codes se dégradent très significativement. Nous étudions tout d’abord les différentes solutions possibles pour modéliser les bruits impulsifs. Dans le cas des interférences d’accès multiples qui apparaissent dans les réseaux ad hoc et les réseaux de capteurs, il nous semble approprié de choisir les distributions alpha-stables. Généralisation de la gaussienne, stables par convolution, elles peuvent être validées théoriquement dans plusieurs situations.Nous déterminons alors la capacité de l’environnement α-stable et montrons par une approche asymptotique que les codes LDPC dans cet environnement sont bons mais qu’une simple opération linéaire à l’entrée du décodeur ne permet pas d’obtenir de bonnes performances. Nous avons donc proposé différentes façons de calculer la vraisemblance en entrée du décodeur. L’approche optimale est très complexe à mettre en oeuvre. Nous avons étudié plusieurs approches différentes et en particulier le clipping dont nous avons cherché les paramètres optimaux
The goal of this PhD is to study the performance of LDPC codes in an environment where interference, generated by the network, has not a Gaussian nature but presents an impulsive behavior.A rapid study shows that, if we do not take care, the codes’ performance significantly degrades.In a first step, we study different approaches for impulsive noise modeling. In the case of multiple access interference that disturb communications in ad hoc or sensor networks, the choice of alpha-stable distributions is appropriate. They generalize Gaussian distributions, are stable by convolution and can be theoretically justified in several contexts.We then determine the capacity if the α-stable environment and show using an asymptotic method that LDPC codes in such an environment are efficient but that a simple linear operation on the received samples at the decoder input does not allow to obtain the expected good performance. Consequently we propose several methods to obtain the likelihood ratio necessary at the decoder input. The optimal solution is highly complex to implement. We have studied several other approaches and especially the clipping for which we proposed several approaches to determine the optimal parameters
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Liu, Shuyan. "Lois stables et processus ponctuels : liens et estimation des paramètres." Phd thesis, Université des Sciences et Technologie de Lille - Lille I, 2009. http://tel.archives-ouvertes.fr/tel-00463817.

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L'objectif de cette thèse est d'étendre une méthode d'estimation des paramètres d'une loi stable dans Rd aux lois à queue régulière dans un cône arbitraire. La méthode d'échantillonnage par paquets est modifiée afin d'optimiser la vitesse de convergence des estimateurs. Un nouvel estimateur de la masse totale de mesure spectrale est proposé. Des résultats sur les statistiques d'ordre des lois à queue régulière dans un cône et la loi des grands nombres pour le schéma triangulaire sont établis. La consistance et la normalité asymptotique des estimateurs sont démontrées. La performance des estimateurs est étudiée par simulation. On compare ces estimateurs avec quelques estimateurs connus. Les tableaux de performance sont fournis. La méthode de noyau est utilisée pour estimer la densité d'une mesure spectrale absolument continue d'une loi à queue régulière. On prouve la consistance de l'estimateur dans notre cas particulier. Pour augmenter le nombre de points utilisés dans l'échantillon, on propose une méthode d'estimation utilisant les permutations aléatoires de l'échantillon. La variation régulière a la propriété d'être préservée par plusieurs opérations et transformations. On considère trois sortes de transformations. Des conditions suffisantes pour cette préservation sont proposées et quelques contre-exemples sont présentés. Les modèles de lois stables et de lois à queue lourde sont très utilisés dans plusieurs domaines d'application. On considère deux jeux de données réelles : les cours des 30 valeurs de l'indice DJIA et les perturbations planétaires des comètes du nuage de Oort. En appliquant la méthode d'estimation présentée on obtient des descriptions statistiques de ces données.
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Eyi-Minko, Frédéric. "Propriétés des processus max-stables : théorèmes limites, lois conditionnelles et mélange fort." Thesis, Poitiers, 2013. http://www.theses.fr/2013POIT2282/document.

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Le thème de cette thèse est la théorie spatiale des valeurs extrêmes, et les objets principalement étudiés sont les processus max-stables à trajectoires continues. Nous commençons par déterminer la convergence des maximums de processus stochastiques indépendants, en utilisant la convergence de mesures empiriques vers des processus ponctuels de Poisson. Ensuite, nous déterminons les lois conditionnelles des processus max infiniment divisibles (max-i.d). La représentation des processus max-i.d par des processus ponctuels de Poisson permet l'introduction de notions telles que les fonctions extrémales et le hitting scénario qui permettent d'aboutir au résultat. Les processus max-stables étant des processus max-i.d, nous proposons un algorithme de simulation conditionnelle pour les champs max-stables puis nous l'utilisons pour des applications avec des données de précipitations autour de Zurich et de températures en Suisse. Nous trouvons aussi, une majoration du coefficient de β-mélange entre les restrictions d'un processus max-i.d sur deux sous-ensembles fermés et disjoints d'un espace métrique localement compact. Cette majoration permet d'obtenir de nouveaux critères pour le théorème de la limite central des processus stationnaires mélangeant. Enfin, nous terminons en démontrant qu'un processus stationnaire max-stable vérifiant la propriété de Markov est, quitte à renverser le temps, un processus max-autorégressif d’ordre 1
The theme of this thesis is spatial extreme value theory and we focus on continuous max-stable processes. We begin with the convergence of the maximum of independent stochastic processes, by using the convergence of empirical measures to Poisson point processes. After that, we determine the regular conditional distributions of max infinitely divisible (max-i.d) processes. The representation of max-i.d. processes by Poisson point processes allows us to introduce the notions of extremal functions and hitting scenario. Our result relies on these new notions. Max-stable processes are max-i.d. processes, so we give an algorithm for conditional sampling and give an application to extreme precipitations around Zurich and extreme temperatures in Switzerland. We also find a upper bound for the β-mixing coefficient between the restrictions of a max-i.d. process on two disjoint closed subsets of a locally compact metric space. This entails a central limit theorem for stationary max-i.d processes. Finally, we prove that the class of stationary maxstable processes with the Markov property is equal, up to time reversal, to the class of stationary max-autoregressive processes of order 1
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Jaoua, Nouha. "Estimation Bayésienne non Paramétrique de Systèmes Dynamiques en Présence de Bruits Alpha-Stables." Phd thesis, Ecole Centrale de Lille, 2013. http://tel.archives-ouvertes.fr/tel-00929691.

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Dans un nombre croissant d'applications, les perturbations rencontrées s'éloignent fortement des modèles classiques qui les modélisent par une gaussienne ou un mélange de gaussiennes. C'est en particulier le cas des bruits impulsifs que nous rencontrons dans plusieurs domaines, notamment celui des télécommunications. Dans ce cas, une modélisation mieux adaptée peut reposer sur les distributions alpha-stables. C'est dans ce cadre que s'inscrit le travail de cette thèse dont l'objectif est de concevoir de nouvelles méthodes robustes pour l'estimation conjointe état-bruit dans des environnements impulsifs. L'inférence est réalisée dans un cadre bayésien en utilisant les méthodes de Monte Carlo séquentielles. Dans un premier temps, cette problématique a été abordée dans le contexte des systèmes de transmission OFDM en supposant que les distorsions du canal sont modélisées par des distributions alpha-stables symétriques. Un algorithme de Monte Carlo séquentiel a été proposé pour l'estimation conjointe des symboles OFDM émis et des paramètres du bruit $\alpha$-stable. Ensuite, cette problématique a été abordée dans un cadre applicatif plus large, celui des systèmes non linéaires. Une approche bayésienne non paramétrique fondée sur la modélisation du bruit alpha-stable par des mélanges de processus de Dirichlet a été proposée. Des filtres particulaires basés sur des densités d'importance efficaces sont développés pour l'estimation conjointe du signal et des densités de probabilité des bruits
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Fries, Sébastien. "Anticipative alpha-stable linear processes for time series analysis : conditional dynamics and estimation." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLG005/document.

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Dans le contexte des séries temporelles linéaires, on étudie les processus strictement stationnaires dits anticipatifs dépendant potentiellement de tous les termes d'une suite d'erreurs alpha-stables indépendantes et identiquement distribuées.On considère en premier lieu les processus autoregressifs (AR) et l'on montre que des moments conditionnels d'ordres plus élevés que les moments marginaux existent dès lors que le polynôme caractéristique admet au moins une racine à l'intérieur du cercle unité.Des formules fermées sont obtenues pour les moments d'ordre un et deux dans des cas particuliers.On montre que la méthode des moindres carrés permet d'estimer une représentation all-pass causale du processus dont la validité peut être vérifiée par un test de type portmanteau, et l'on propose une méthode fondée sur des propriétés d'extreme clustering pour retrouver la représentation AR originale.L'AR(1) stable anticipatif est étudié en détails dans le cadre des vecteurs stables bivariés et des formes fonctionnelles pour les quatre premiers moments conditionnels sont obtenues pour toute paramétrisation admissible.Lors des évènements extrêmes, il est montré que ces moments deviennent équivalents à ceux d'une distribution de Bernoulli chargeant deux évolutions futures opposées: accroissement exponentiel ou retour aux valeurs centrales.Des résultats parallèles sont obtenus pour l'analogue de l'AR(1) en temps continu, le processus d'Ornstein-Uhlenbeck stable anticipatif.Pour des moyennes mobiles alpha-stables infinies, la distribution conditionnelle des chemins futurs sachant la trajectoire passée est obtenue lors des évènements extrêmes par le biais d'une nouvelle représentation des vecteurs stables multivariés sur des cylindres unités relatifs à des semi-normes.Contrairement aux normes, ce type de représentation donne lieu à une propriété de variations régulières des queues de distribution utilisable dans un contexte de prévision, mais tout vecteur stable n'admet pas une telle représentation. Une caractérisation est donnée et l'on montre qu'un chemin fini de moyenne mobile alpha-stable sera représentable pourvu que le processus soit "suffisamment anticipatif".L'approche s'étend aux processus résultant de la combinaison linéaire de moyennes mobiles alpha-stables, et la distribution conditionnelle des chemins futurs s'interprète naturellement en termes de reconnaissance de formes
In the framework of linear time series analysis, we study a class of so-called anticipative strictly stationary processes potentially depending on all the terms of an independent and identically distributed alpha-stable errors sequence.Focusing first on autoregressive (AR) processes, it is shown that higher order conditional moments than marginal ones exist provided the characteristic polynomials admits at least one root inside the unit circle. The forms of the first and second order moments are obtained in special cases.The least squares method is shown to provide a consistent estimator of an all-pass causal representation of the process, the validity of which can be tested by a portmanteau-type test. A method based on extreme residuals clustering is proposed to determine the original AR representation.The anticipative stable AR(1) is studied in details in the framework of bivariate alpha-stable random vectors and the functional forms of its first four conditional moments are obtained under any admissible parameterisation.It is shown that during extreme events, these moments become equivalent to those of a two-point distribution charging two polarly-opposite future paths: exponential growth or collapse.Parallel results are obtained for the continuous time counterpart of the AR(1), the anticipative stable Ornstein-Uhlenbeck process.For infinite alpha-stable moving averages, the conditional distribution of future paths given the observed past trajectory during extreme events is derived on the basis of a new representation of stable random vectors on unit cylinders relative to semi-norms.Contrary to the case of norms, such representation yield a multivariate regularly varying tails property appropriate for prediction purposes, but not all stable vectors admit such a representation.A characterisation is provided and it is shown that finite length paths of a stable moving average admit such representation provided the process is "anticipative enough".Processes resulting from the linear combination of stable moving averages are encompassed, and the conditional distribution has a natural interpretation in terms of pattern identification
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Béranger, Boris. "Modélisation de la structure de dépendance d'extrêmes multivariés et spatiaux." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066004/document.

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La prédiction de futurs évènements extrêmes est d’un grand intérêt dans de nombreux domaines tels que l’environnement ou la gestion des risques. Alors que la théorie des valeurs extrêmes univariées est bien connue, la complexité s’accroît lorsque l’on s’intéresse au comportement joint d’extrêmes de plusieurs variables. Un intérêt particulier est porté aux évènements de nature spatiale, définissant le cadre d’un nombre infini de dimensions. Sous l’hypothèse que ces évènements soient marginalement extrêmes, nous focalisons sur la structure de dépendance qui les lie. Dans un premier temps, nous faisons une revue des modèles paramétriques de dépendance dans le cadre multivarié et présentons différentes méthodes d’estimation. Les processus maxstables permettent l’extension au contexte spatial. Nous dérivons la loi en dimension finie du célèbre modèle de Brown- Resnick, permettant de faire de l’inférence par des méthodes de vraisemblance ou de vraisemblance composée. Nous utilisons ensuite des lois asymétriques afin de définir la représentation spectrale d’un modèle plus large : le modèle Extremal Skew-t, généralisant la plupart des modèles présents dans la littérature. Ce modèle a l’agréable propriété d’être asymétrique et non-stationnaire, deux notions présentées par les évènements environnementaux spatiaux. Ce dernier permet un large spectre de structures de dépendance. Les indicateurs de dépendance sont obtenus en utilisant la loi en dimension finie.Enfin, nous présentons une méthode d’estimation non-paramétrique par noyau pour les queues de distributions et l’appliquons à la sélection de modèles. Nous illustrons notre méthode à partir de l’exemple de modèles climatiques
Projection of future extreme events is a major issue in a large number of areas including the environment and risk management. Although univariate extreme value theory is well understood, there is an increase in complexity when trying to understand the joint extreme behavior between two or more variables. Particular interest is given to events that are spatial by nature and which define the context of infinite dimensions. Under the assumption that events correspond marginally to univariate extremes, the main focus is then on the dependence structure that links them. First, we provide a review of parametric dependence models in the multivariate framework and illustrate different estimation strategies. The spatial extension of multivariate extremes is introduced through max-stable processes. We derive the finite-dimensional distribution of the widely used Brown-Resnick model which permits inference via full and composite likelihood methods. We then use Skew-symmetric distributions to develop a spectral representation of a wider max-stable model: the extremal Skew-t model from which most models available in the literature can be recovered. This model has the nice advantages of exhibiting skewness and nonstationarity, two properties often held by environmental spatial events. The latter enables a larger spectrum of dependence structures. Indicators of extremal dependence can be calculated using its finite-dimensional distribution. Finally, we introduce a kernel based non-parametric estimation procedure for univariate and multivariate tail density and apply it for model selection. Our method is illustrated by the example of selection of physical climate models
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Finke, Jorge. "Stable emergent ideal free distributions." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1172757689.

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Pivato, Marcus. "Analytical methods for multivariate stable probability distributions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ63698.pdf.

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Jama, Siphamandla. "An alternative model for multivariate stable distributions." Master's thesis, University of Cape Town, 2009. http://hdl.handle.net/11427/8959.

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Includes bibliographical references (leaves 52-55).
As the title, "An Alternative Model for Multivariate Stable Distributions", depicts, this thesis draws from the methodology of [J36] and derives an alternative to the sub-Gaussian alpha-stable distribution as another model for multivariate stable data without using the spectral measure as a dependence structure. From our investigation, firstly, we echo that the assumption of "Gaussianity" must be rejected, as a model for, particularly, high frequency financial data based on evidence from the Johannesburg Stock Exchange (JSE). Secondly, the introduced technique adequately models bivariate return data far better than the Gaussian model. We argue that unlike the sub-Gaussian stable and the model involving a spectral measure this technique is not subject to estimation of a joint index of stability, as such it may remain a superior alternative in empirical stable distribution theory. Thirdly, we confirm that the Gaussian Value-at-Risk and Conditional Value-at-Risk measures are more optimistic and misleading while their stable counterparts are more informative and reasonable. Fourthly, our results confirm that stable distributions are more appropriate for portfolio optimization than the Gaussian framework.
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Books on the topic "Distributions stables"

1

Grabchak, Michael. Tempered Stable Distributions. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-24927-8.

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Nolan, John P. Univariate Stable Distributions. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52915-4.

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One-dimensional stable distributions. Provindence, R.I: American Mathematical Society, 1986.

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Principles of stable isotope distribution. New York: Oxford University Press, 1999.

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Min, Shao, ed. Signal processing with alpha-stable distributions and applications. New York: Wiley, 1995.

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Christoph, Gerd. Convergence theorems with a stable limit law. Berlin: Akademie Verlag, 1992.

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Probability in Banach spaces--stable and infinitely divisible distributions. Chichester: Wiley, 1986.

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Linde, Werner. Probability in Banach spaces: Stable and infinitely divisible distributions. Chichester: Wiley, 1986.

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S, Taqqu Murad, ed. Stable non-Gaussian random processes: Stochastic models with infinite variance. New York: Chapman & Hall, 1994.

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Bager-Sjögren, Lars. A comparison between OLS and LAV: An empirical analysis and simulations using stable distributions. Gothenburg: Departement [sic] of Economics, University of Gothenburg, 1993.

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Book chapters on the topic "Distributions stables"

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Nolan, John P. "Basic Properties of Univariate Stable Distributions." In Univariate Stable Distributions, 1–23. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52915-4_1.

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Nolan, John P. "Modeling with Stable Distributions." In Univariate Stable Distributions, 25–52. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52915-4_2.

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Nolan, John P. "Univariate Estimation." In Univariate Stable Distributions, 159–222. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52915-4_4.

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Nolan, John P. "Signal Processing with Stable Distributions." In Univariate Stable Distributions, 239–53. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52915-4_6.

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Nolan, John P. "Technical Results for Univariate Stable Distributions." In Univariate Stable Distributions, 53–157. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52915-4_3.

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Nolan, John P. "Related Distributions." In Univariate Stable Distributions, 255–66. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52915-4_7.

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Nolan, John P. "Stable Regression." In Univariate Stable Distributions, 223–38. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-52915-4_5.

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Obuchowicz, Andrzej. "Stable Distributions." In Stable Mutations for Evolutionary Algorithms, 23–48. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01548-0_3.

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Li, Ping. "Stable Distribution." In Encyclopedia of Database Systems, 3690–94. New York, NY: Springer New York, 2018. http://dx.doi.org/10.1007/978-1-4614-8265-9_367.

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Li, Ping. "Stable Distribution." In Encyclopedia of Database Systems, 2768–71. Boston, MA: Springer US, 2009. http://dx.doi.org/10.1007/978-0-387-39940-9_367.

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Conference papers on the topic "Distributions stables"

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Khuwuthyakorn, Pattaraporn, Antonio Robles-Kelly, and Jun Zhou. "Texture Descriptors via Stable Distributions." In 2008 Digital Image Computing: Techniques and Applications. IEEE, 2008. http://dx.doi.org/10.1109/dicta.2008.93.

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Nolan, John P. "Metrics for multivariate stable distributions." In Stability in Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc90-0-6.

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Jianhua Wang and Dan Li. "Stable distribution and option pricing." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002644.

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Makarov, Vasiliy, and Tahir Alizada. "Stable distributions conforming to kinetic equations." In 2012 IV International Conference "Problems of Cybernetics and Informatics" (PCI). IEEE, 2012. http://dx.doi.org/10.1109/icpci.2012.6486421.

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Mihaylova, L., P. Brasnett, A. Achim, D. Bull, and N. Canagarajah. "Particle filtering with alpha-stable distributions." In 2005 Microwave Electronics: Measurements, Identification, Applications. IEEE, 2005. http://dx.doi.org/10.1109/ssp.2005.1628625.

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Shojaei, S. R. Hosseini, V. Nassiri, Gh R. Mohammadian, A. Mohammadpour, Ali Mohammad-Djafari, Jean-François Bercher, and Pierre Bessiére. "Mixture of Skewed α-Stable Distributions." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 30th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP, 2011. http://dx.doi.org/10.1063/1.3573609.

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Shokripour, Mona, Vahid Nassiri, Adel Mohammadpour, Ali Mohammad-Djafari, Jean-François Bercher, and Pierre Bessiére. "Bayesian Inference for Skewed Stable Distributions." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 30th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP, 2011. http://dx.doi.org/10.1063/1.3573610.

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Fiche, A., A. Martin, J. C. Cexus, and A. Khenchaf. "Continuous belief functions and α-stable distributions." In 2010 13th International Conference on Information Fusion (FUSION 2010). IEEE, 2010. http://dx.doi.org/10.1109/icif.2010.5711934.

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Achim, Alin M. "Bivariate wavelet shrinkage using alpha-stable distributions." In Optics & Photonics 2005, edited by Manos Papadakis, Andrew F. Laine, and Michael A. Unser. SPIE, 2005. http://dx.doi.org/10.1117/12.618404.

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Senjyu, Tomonobu, Yuri Yonaha, and Atsushi Yona. "Stable operation for distributed generators on distribution system using UPFC." In 2009 Transmission & Distribution Conference & Exposition: Asia and Pacific. IEEE, 2009. http://dx.doi.org/10.1109/td-asia.2009.5357002.

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Reports on the topic "Distributions stables"

1

Nolan, John P. Efficient Methods for Stable Distributions. Fort Belvoir, VA: Defense Technical Information Center, June 2003. http://dx.doi.org/10.21236/ada415451.

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Nolan, John P. Efficient Numerical Methods for Stable Distributions. Fort Belvoir, VA: Defense Technical Information Center, June 2003. http://dx.doi.org/10.21236/ada434737.

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Bell, W. A., and J. G. Tracy. Stable isotope separation in calutrons: Forty years of production and distribution. Office of Scientific and Technical Information (OSTI), November 1987. http://dx.doi.org/10.2172/5903249.

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Martinez, A., W. Spall, and B. Smith. A gas chromatograph/mass spectrometry method for determining isotopic distributions in organic compounds used in the chemical approach to stable isotope separation. Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/5114527.

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Nolan, Brian, Brenda Gannon, Richard Layte, Dorothy Watson, Christopher T. Whelan, and James Williams. Monitoring Poverty Trends in Ireland: Results from the 2000 Living in Ireland survey. ESRI, July 2002. http://dx.doi.org/10.26504/prs45.

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This study is the latest in a series monitoring the evolution of poverty, based on data gathered by The ESRI in the Living in Ireland Surveys since 1994. These have allowed progress towards achieving the targets set out in the National Anti Poverty Strategy since 1997 to be assessed. The present study provides an updated picture using results from the 2000 round of the Living in Ireland survey. The numbers interviewed in the 2000 Living in Ireland survey were enhanced substantially, to compensate for attrition in the panel survey since it commenced in 1994. Individual interviews were conducted with 8,056 respondents. Relative income poverty lines do not on their own provide a satisfactory measure of exclusion due to lack of resources, but do nonetheless produce important key indicators of medium to long-term background trends. The numbers falling below relative income poverty lines were most often higher in 2000 than in 1997 or 1994. The income gap for those falling below these thresholds also increased. By contrast, the percentage of persons falling below income lines indexed only to prices (rather than average income) since 1994 or 1997 fell sharply, reflecting the pronounced real income growth throughout the distribution between then and 2000. This contrast points to the fundamental factors at work over this highly unusual period: unemployment fell very sharply and substantial real income growth was seen throughout the distribution, including social welfare payments, but these lagged behind income from work and property so social welfare recipients were more likely to fall below thresholds linked to average income. The study shows an increasing probability of falling below key relative income thresholds for single person households, those affected by illness or disability, and for those who are aged 65 or over - many of whom rely on social welfare support. Those in households where the reference person is unemployed still face a relatively high risk of falling below the income thresholds but continue to decline as a proportion of all those below the lines. Women face a higher risk of falling below those lines than men, but this gap was marked among the elderly. The study shows a marked decline in deprivation levels across different household types. As a result consistent poverty, that is the numbers both below relative income poverty lines and experiencing basic deprivation, also declined sharply. Those living in households comprising one adult with children continue to face a particularly high risk of consistent poverty, followed by those in families with two adults and four or more children. The percentage of adults in households below 70 per cent of median income and experiencing basic deprivation was seen to have fallen from 9 per cent in 1997 to about 4 per cent, while the percentage of children in such households fell from 15 per cent to 8 per cent. Women aged 65 or over faced a significantly higher risk of consistent poverty than men of that age. Up to 2000, the set of eight basic deprivation items included in the measure of consistent poverty were unchanged, so it was important to assess whether they were still capturing what would be widely seen as generalised deprivation. Factor analysis suggested that the structuring of deprivation items into the different dimensions has remained remarkably stable over time. Combining low income with the original set of basic deprivation indicators did still appear to identify a set of households experiencing generalised deprivation as a result of prolonged constraints in terms of command over resources, and distinguished from those experiencing other types of deprivation. However, on its own this does not tell the whole story - like purely relative income measures - nor does it necessarily remain the most appropriate set of indicators looking forward. Finally, it is argued that it would now be appropriate to expand the range of monitoring tools to include alternative poverty measures incorporating income and deprivation. Levels of deprivation for some of the items included in the original basic set were so low by 2000 that further progress will be difficult to capture empirically. This represents a remarkable achievement in a short space of time, but poverty is invariably reconstituted in terms of new and emerging social needs in a context of higher societal living standards and expectations. An alternative set of basic deprivation indicators and measure of consistent poverty is presented, which would be more likely to capture key trends over the next number of years. This has implications for the approach adopted in monitoring the National Anti-Poverty Strategy. Monitoring over the period to 2007 should take a broader focus than the consistent poverty measure as constructed to date, with attention also paid to both relative income and to consistent poverty with the amended set of indicators identified here.
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