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Academic literature on the topic 'Variance Gamma Model'

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Published: 4 June 2021
Last updated: 3 February 2022

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Journal articles on the topic "Variance Gamma Model"

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Carr, P., and A. Itkin. "Geometric Local Variance Gamma Model." Journal of Derivatives 27, no. 2 (September 11, 2019): 7–30. http://dx.doi.org/10.3905/jod.2019.1.084.

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Schoutens, Wim, and Geert Van Damme. "The β-variance gamma model." Review of Derivatives Research 14, no. 3 (July 24, 2010): 263–82. http://dx.doi.org/10.1007/s11147-010-9057-y.

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Fry, John, Oliver Smart, Jean-Philippe Serbera, and Bernhard Klar. "A Variance Gamma model for Rugby Union matches." Journal of Quantitative Analysis in Sports 17, no. 1 (May 5, 2020): 67–75. http://dx.doi.org/10.1515/jqas-2019-0088.

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Abstract Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.
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SEMERARO, PATRIZIA. "A MULTIVARIATE VARIANCE GAMMA MODEL FOR FINANCIAL APPLICATIONS." International Journal of Theoretical and Applied Finance 11, no. 01 (February 2008): 1–18. http://dx.doi.org/10.1142/s0219024908004701.

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In this paper we subordinate a multivariate Brownian motion with independent components by a multivariate gamma subordinator. The resulting process is a generalization of the bivariate variance gamma process proposed by Madan and Seneta [7], mentioned in Cont and Tankov [4] and calibrated in Luciano and Schoutens [5] as a price process. Our main contribution here is to introduce a multivariate subordinator with gamma margins. We investigate the process, determine its Lévy triplet and analyze its dependence structure. At the end we propose an exponential Lévy price model.
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Ivanov, Roman V. "On risk measuring in the variance-gamma model." Statistics & Risk Modeling 35, no. 1-2 (January 1, 2018): 23–33. http://dx.doi.org/10.1515/strm-2017-0008.

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AbstractIn this paper, we discuss the problem of calculating the primary risk measures in the variance-gamma model. A portfolio of investments in a one-period setting is considered. It is supposed that the investment returns are dependent on each other. In terms of the variance-gamma model, we assume that there are relations in both groups of the normal random variables and the gamma stochastic volatilities. The value at risk, the expected shortfall and the entropic monetary risk measures are discussed. The obtained analytical expressions are based on values of hypergeometric functions.
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Orzechowski, Arkadiusz. "PRICING EUROPEAN OPTIONS IN THE VARIANCE GAMMA MODEL." Metody Ilościowe w Badaniach Ekonomicznych 20, no. 1 (June 10, 2019): 45–53. http://dx.doi.org/10.22630/mibe.2019.20.1.5.

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Cheng, Min, and Yubo Li. "Convertible Bond Pricing Based on Variance Gamma Model." Saudi Journal of Economics and Finance 4, no. 6 (June 24, 2020): 287–92. http://dx.doi.org/10.36348/sjef.2020.v04i06.015.

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Seneta, Eugene. "Fitting the variance-gamma model to financial data." Journal of Applied Probability 41, A (2004): 177–87. http://dx.doi.org/10.1017/s0021900200112288.

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This paper has as its main theme the fitting in practice of the variance-gamma distribution, which allows for skewness, by moment methods. This fitting procedure allows for possible dependence of increments in log returns, while retaining their stationarity. It is intended as a step in a partial synthesis of some ideas of Madan, Carr and Chang (1998) and of Heyde (1999). Standard estimation and hypothesis-testing theory depends on a large sample of observations which are independently as well as identically distributed and consequently may give inappropriate conclusions in the presence of dependence.
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AGUILAR, JEAN-PHILIPPE. "SOME PRICING TOOLS FOR THE VARIANCE GAMMA MODEL." International Journal of Theoretical and Applied Finance 23, no. 04 (June 2020): 2050025. http://dx.doi.org/10.1142/s0219024920500259.

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We establish several closed pricing formulas for various path-independent payoffs, under an exponential Lévy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools from Mellin transform theory as well as from multidimensional complex analysis. Particular focus is made on the symmetric process, but extension to the asymmetric process is also provided. Speed of convergence and comparison with numerical methods (Fourier transform, quadrature approximations, Monte Carlo simulations) are also discussed; notable feature is the accelerated convergence of the series for short-term options, which constitutes an interesting improvement of numerical Fourier inversion techniques.
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Seneta, Eugene. "Fitting the variance-gamma model to financial data." Journal of Applied Probability 41, A (2004): 177–87. http://dx.doi.org/10.1239/jap/1082552198.

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This paper has as its main theme the fitting in practice of the variance-gamma distribution, which allows for skewness, by moment methods. This fitting procedure allows for possible dependence of increments in log returns, while retaining their stationarity. It is intended as a step in a partial synthesis of some ideas of Madan, Carr and Chang (1998) and of Heyde (1999). Standard estimation and hypothesis-testing theory depends on a large sample of observations which are independently as well as identically distributed and consequently may give inappropriate conclusions in the presence of dependence.
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Dissertations / Theses on the topic "Variance Gamma Model"

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Finlay, Richard. "The Variance Gamma (VG) Model with Long Range Dependence." University of Sydney, 2009. http://hdl.handle.net/2123/5434.

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Doctor of Philosophy (PhD)
This thesis mainly builds on the Variance Gamma (VG) model for financial assets over time of Madan & Seneta (1990) and Madan, Carr & Chang (1998), although the model based on the t distribution championed in Heyde & Leonenko (2005) is also given attention. The primary contribution of the thesis is the development of VG models, and the extension of t models, which accommodate a dependence structure in asset price returns. In particular it has become increasingly clear that while returns (log price increments) of historical financial asset time series appear as a reasonable approximation of independent and identically distributed data, squared and absolute returns do not. In fact squared and absolute returns show evidence of being long range dependent through time, with autocorrelation functions that are still significant after 50 to 100 lags. Given this evidence against the assumption of independent returns, it is important that models for financial assets be able to accommodate a dependence structure.
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Moravec, Radek. "Oceňování opcí a variance gama proces." Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-18707.

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The submitted work deals with option pricing. Mathematical approach is immediately followed by an economic interpretation. The main problem is to model the underlying uncertainities driving the stock price. Using two well-known valuation models, binomial model and Black-Scholes model, we explain basic principles, especially risk neutral pricing. Due to the empirical biases new models have been developped, based on pure jump process. Variance gamma process and its special symmetric case are presented.
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Febrer, Pedro Maria Ulisses dos Santos Jalhay. "Residue sum formula for pricing options under the variance Gamma Model." Master's thesis, Instituto Superior de Economia e Gestão, 2020. http://hdl.handle.net/10400.5/20802.

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Mestrado em Mathematical Finance
O resultado principal desta dissertação é a demonstração da fórmula de serie de soma tripla para o preço de uma opção Europeia induzido por um processo Variance Gamma. Com esta intenção, apresentamos certas propriedades e noções sobre processos de Lévy e análise complexa multidimensional, dando ênfase à aplicação do cálculo de resíduos ao integral Mellin-Barnes. Subsequentemente, iremos construir a representação na forma do integral Mellin-Barnes, em C^3, para o preço de uma opção e, apoiados pelo anteriormente mencionado cálculo de resíduos, deduziremos a representação em serie de soma tripla para o preço de uma opção Europeia e os seus correspondentes gregos. Para terminar, dando uso à nova formula, serão computados e discutidos alguns valores para um caso de estudo particular.
The main result of this dissertation is the proof of the triple sum series formula for the price of an European call option driven by the Variance Gamma process. With this intention, we present some notions and properties of Lévy processes and multidimensional complex analysis, with emphasis on the application of residue calculus to the Mellin-Barnes integral. Subsequently, we construct the Mellin-Barnes integral representation, in C^3, for the price of the option and, buttressed with the aforementioned residue calculus, we deduce the triple sum series representation for the price of the European option and its corresponding greeks. Finally, with the use of the new formula, some values for a particular case study are computed and discussed.
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Lee, Brendan Chee-Seng Banking &amp Finance Australian School of Business UNSW. "Incorporating discontinuities in value-at-risk via the poisson jump diffusion model and variance gamma model." Awarded by:University of New South Wales, 2007. http://handle.unsw.edu.au/1959.4/37201.

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We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.
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Lee, Mou Chin. "An empirical test of variance gamma options pricing model on Hang Seng index options." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/263.

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Anar, Hatice. "Credit Risk Modeling And Credit Default Swap Pricing Under Variance Gamma Process." Master's thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/3/12609840/index.pdf.

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In this thesis, the structural model in credit risk and the credit derivatives is studied under both Black-Scholes setting and Variance Gamma (VG) setting. Using a Variance Gamma process, the distribution of the firm value process becomes asymmetric and leptokurtic. Also, the jump structure of VG processes allows random default times of the reference entities. Among structural models, the most emphasis is made on the Black-Cox model by building a relation between the survival probabilities of the Black-Cox model and the value of a binary down and out barrier option. The survival probabilities under VG setting are calculated via a Partial Integro Differential Equation (PIDE). Some applications of binary down and out barrier options, default probabilities and Credit Default Swap par spreads are also illustrated in this study.
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Oliveira, Izabela Regina Cardoso de. "Modeling strategies for complex hierarchical and overdispersed data in the life sciences." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-12082014-105135/.

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In this work, we study the so-called combined models, generalized linear mixed models with extension to allow for overdispersion, in the context of genetics and breeding. Such flexible models accommodates cluster-induced correlation and overdispersion through two separate sets of random effects and contain as special cases the generalized linear mixed models (GLMM) on the one hand, and commonly known overdispersion models on the other. We use such models while obtaining heritability coefficients for non-Gaussian characters. Heritability is one of the many important concepts that are often quantified upon fitting a model to hierarchical data. It is often of importance in plant and animal breeding. Knowledge of this attribute is useful to quantify the magnitude of improvement in the population. For data where linear models can be used, this attribute is conveniently defined as a ratio of variance components. Matters are less simple for non-Gaussian outcomes. The focus is on time-to-event and count traits, where the Weibull-Gamma-Normal and Poisson-Gamma-Normal models are used. The resulting expressions are sufficiently simple and appealing, in particular in special cases, to be of practical value. The proposed methodologies are illustrated using data from animal and plant breeding. Furthermore, attention is given to the occurrence of negative estimates of variance components in the Poisson-Gamma-Normal model. The occurrence of negative variance components in linear mixed models (LMM) has received a certain amount of attention in the literature whereas almost no work has been done for GLMM. This phenomenon can be confusing at first sight because, by definition, variances themselves are non-negative quantities. However, this is a well understood phenomenon in the context of linear mixed modeling, where one will have to make a choice between a hierarchical and a marginal view. The variance components of the combined model for count outcomes are studied theoretically and the plant breeding study used as illustration underscores that this phenomenon can be common in applied research. We also call attention to the performance of different estimation methods, because not all available methods are capable of extending the parameter space of the variance components. Then, when there is a need for inference on such components and they are expected to be negative, the accuracy of the method is not the only characteristic to be considered.
Neste trabalho foram estudados os chamados modelos combinados, modelos lineares generalizados mistos com extensão para acomodar superdispersão, no contexto de genética e melhoramento. Esses modelos flexíveis acomodam correlação induzida por agrupamento e superdispersão por meio de dois conjuntos separados de efeitos aleatórios e contem como casos especiais os modelos lineares generalizados mistos (MLGM) e os modelos de superdispersão comumente conhecidos. Tais modelos são usados na obtenção do coeficiente de herdabilidade para caracteres não Gaussianos. Herdabilidade é um dos vários importantes conceitos que são frequentemente quantificados com o ajuste de um modelo a dados hierárquicos. Ela é usualmente importante no melhoramento vegetal e animal. Conhecer esse atributo é útil para quantificar a magnitude do ganho na população. Para dados em que modelos lineares podem ser usados, esse atributo é convenientemente definido como uma razão de componentes de variância. Os problemas são menos simples para respostas não Gaussianas. O foco aqui é em características do tipo tempo-até-evento e contagem, em que os modelosWeibull-Gama-Normal e Poisson-Gama-Normal são usados. As expressões resultantes são suficientemente simples e atrativas, em particular nos casos especiais, pelo valor prático. As metodologias propostas são ilustradas usando dados de melhoramento animal e vegetal. Além disso, a atenção é voltada à ocorrência de estimativas negativas de componentes de variância no modelo Poisson-Gama- Normal. A ocorrência de componentes de variância negativos em modelos lineares mistos (MLM) tem recebido certa atenção na literatura enquanto quase nenhum trabalho tem sido feito para MLGM. Esse fenômeno pode ser confuso a princípio porque, por definição, variâncias são quantidades não-negativas. Entretanto, este é um fenômeno bem compreendido no contexto de modelagem linear mista, em que a escolha deverá ser feita entre uma interpretação hierárquica ou marginal. Os componentes de variância do modelo combinado para respostas de contagem são estudados teoricamente e o estudo de melhoramento vegetal usado como ilustração confirma que esse fenômeno pode ser comum em pesquisas aplicadas. A atenção também é voltada ao desempenho de diferentes métodos de estimação, porque nem todos aqueles disponíveis são capazes de estender o espaço paramétrico dos componentes de variância. Então, quando há a necessidade de inferência de tais componentes e é esperado que eles sejam negativos, a acurácia do método de estimação não é a única característica a ser considerada.
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Mamane, Salha. "Lois de Wishart sur les cônes convexes." Thesis, Angers, 2017. http://www.theses.fr/2017ANGE0003/document.

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En analyse multivariée de données de grande dimension, les lois de Wishart définies dans le contexte des modèles graphiques revêtent une grande importance car elles procurent parcimonie et modularité. Dans le contexte des modèles graphiques Gaussiens régis par un graphe G, les lois de Wishart peuvent être définies sur deux restrictions alternatives du cône des matrices symétriques définies positives : le cône PG des matrices symétriques définies positives x satisfaisant xij=0, pour tous sommets i et j non adjacents, et son cône dual QG. Dans cette thèse, nous proposons une construction harmonieuse de familles exponentielles de lois de Wishart sur les cônes PG et QG. Elle se focalise sur les modèles graphiques d'interactions des plus proches voisins qui présentent l'avantage d'être relativement simples tout en incluant des exemples de tous les cas particuliers intéressants: le cas univarié, un cas d'un cône symétrique, un cas d'un cône homogène non symétrique, et une infinité de cas de cônes non-homogènes. Notre méthode, simple, se fonde sur l'analyse sur les cônes convexes. Les lois de Wishart sur QAn sont définies à travers la fonction gamma sur QAn et les lois de Wishart sur PAn sont définies comme la famille de Diaconis- Ylvisaker conjuguée. Ensuite, les méthodes développées sont utilisées pour résoudre la conjecture de Letac- Massam sur l'ensemble des paramètres de la loi de Wishart sur QAn. Cette thèse étudie aussi les sousmodèles, paramétrés par un segment dans M, d'une famille exponentielle paramétrée par le domaine des moyennes M
In the framework of Gaussian graphical models governed by a graph G, Wishart distributions can be defined on two alternative restrictions of the cone of symmetric positive definite matrices: the cone PG of symmetric positive definite matrices x satisfying xij=0 for all non-adjacent vertices i and j and its dual cone QG. In this thesis, we provide a harmonious construction of Wishart exponential families in graphical models. Our simple method is based on analysis on convex cones. The focus is on nearest neighbours interactions graphical models, governed by a graph An, which have the advantage of being relatively simple while including all particular cases of interest such as the univariate case, a symmetric cone case, a nonsymmetric homogeneous cone case and an infinite number of non-homogeneous cone cases. The Wishart distributions on QAn are constructed as the exponential family generated from the gamma function on QAn. The Wishart distributions on PAn are then constructed as the Diaconis- Ylvisaker conjugate family for the exponential family of Wishart distributions on QAn. The developed methods are then used to solve the Letac-Massam Conjecture on the set of parameters of type I Wishart distributions on QAn. Finally, we introduce and study exponential families of distributions parametrized by a segment of means with an emphasis on their Fisher information. The focus in on distributions with matrix parameters. The particular cases of Gaussian and Wishart exponential families are further examined
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Kump, Paul. "Passive detection of radionuclides from weak and poorly resolved gamma-ray energy spectra." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/3329.

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Large passive detectors used in screening for special nuclear materials at ports of entry are characterized by poor spectral resolution, making identification of radionuclides a difficult task. Most identification routines, which fit empirical shapes and use derivatives, are impractical in these situations. Here I develop new, physics-based methods to determine the presence of spectral signatures of one or more of a set of isotopes. Gamma-ray counts are modeled as Poisson processes, where the average part is taken to be the model and the difference between the observed gamma-ray counts and the average is considered random noise. In the linear part, the unknown coefficients represent the intensites of the isotopes. Therefore, it is of great interest not to estimate each coefficient, but rather determine if the coefficient is non-zero, corresponding to the presence of the isotope. This thesis provides new selection algorithms, and, since detector data is undoubtedly finite, this unique work emphasizes selection when data is fixed and finite.
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Greenwood, Aaron James. "Spectroscopic Analysis of γ Doradus Variable Stars." Thesis, University of Canterbury. Physics and Astronomy, 2014. http://hdl.handle.net/10092/9216.

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Three γ Doradus-type stars are analysed: HD139095, HD153580, and HD197541. Long-term observation campaigns have been conducted on each star, with over 300 spectra of each star being gathered for analysis using the HERCULES spectrograph at Mount John University Observatory. For each star, cross-correlation techniques were used to obtain representative line profiles for each spectrum. The analysis of these line profiles has resulted in frequency and pulsation mode identifications for these three stars. Abundance analysis has also been performed on HD139095 and HD197541, and their fundamental parameters are confirmed as being consistent with the γ Doradus class of stars. HD153580 and HD197541, previously only candidates for the class, can now be classified as bona fide γ Doradus type stars. The frequencies and modes identified in this thesis will be very useful in constraining future theoretical models, allowing us to better understand and model the interiors of γ Doradus stars.
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Books on the topic "Variance Gamma Model"

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Ma, Xiaofang. Computation of the probability density function and the cumulative distribution function of the generalized gamma variance model. Ottawa: National Library of Canada, 2002.

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Cheng, Russell. Randomized-Parameter Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0013.

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This chapter does not involve non-standard behaviour but is included as a contribution to the broader book theme on model building. The basic idea is to obtain greater flexibility in fitting a standard two-parameter base distribution by multiplying one of its parameters by a one-parameter mixing random variable with mean unity. Absorbing the random effect by integration yields what will be called a randomized parameter (also called compound) distribution depending on all three parameters involved. This chapter collects together a large number of examples where there is a gamma mixing distribution. Their tail behaviour is compared. For the cases where the base distribution is the Pearson Type III or V, the randomized three-parameter model is the Pearson Type VI, providing a different view of the relationship between these distributions previously examined via embeddedness. Fits obtained using some of these models in a real-data example are given.
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Book chapters on the topic "Variance Gamma Model"

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Zhang, Huiming, and Junzo Watada. "Building Fuzzy Variance Gamma Option Pricing Models with Jump Levy Process." In Intelligent Decision Technologies 2017, 105–16. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59424-8_10.

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"Geometric Local Variance Gamma Model." In Fitting Local Volatility, 137–73. WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811212772_0006.

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"An Expanded Local Variance Gamma Model." In Fitting Local Volatility, 101–36. WORLD SCIENTIFIC, 2020. http://dx.doi.org/10.1142/9789811212772_0005.

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Hector, Andy. "Generalized Linear Models." In The New Statistics with R, 195–208. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198798170.003.0015.

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This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with a generalized linear-model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution, where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.
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Ari, Yakup. "Continuous Autoregressive Moving Average Models." In Methodologies and Applications of Computational Statistics for Machine Intelligence, 118–41. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7701-1.ch007.

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The financial time series have a high frequency and the difference between their observations is not regular. Therefore, continuous models can be used instead of discrete-time series models. The purpose of this chapter is to define Lévy-driven continuous autoregressive moving average (CARMA) models and their applications. The CARMA model is an explicit solution to stochastic differential equations, and also, it is analogue to the discrete ARMA models. In order to form a basis for CARMA processes, the structures of discrete-time processes models are examined. Then stochastic differential equations, Lévy processes, compound Poisson processes, and variance gamma processes are defined. Finally, the parameter estimation of CARMA(2,1) is discussed as an example. The most common method for the parameter estimation of the CARMA process is the pseudo maximum likelihood estimation (PMLE) method by mapping the ARMA coefficients to the corresponding estimates of the CARMA coefficients. Furthermore, a simulation study and a real data application are given as examples.
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Elsner, James B., and Thomas H. Jagger. "Bayesian Models." In Hurricane Climatology. Oxford University Press, 2013. http://dx.doi.org/10.1093/oso/9780199827633.003.0016.

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In this chapter, we focus on Bayesian modeling. Information about past hurricanes is available from instruments and written accounts. Written accounts are generally less precise than instrumental observations, which tend to become even more precise as technology advances. Here we show you how to build Bayesian models that make use of the available information while accounting for differences in levels of precision. We begin with a model for U.S. hurricane frequency and finish with a space–time model for basin-wide occurrences. We start with a model for predicting U.S. hurricane activity over the next three decades. The model is useful as a benchmark for climate change studies. The methodology was originally presented in Elsner and Bossak (2001) based on the formalism given in Epstein (1985). As you have seen throughout this book, the arrival of hurricanes on the coast is usefully considered a stochastic process, where the annual counts are described reasonably well by a Poisson distribution. The Poisson distribution is a limiting form of the binomial distribution with no upper bound on the number of occurrences and where the parameter λ characterizes the rate process. Knowledge of λ allows you to make statements about future hurricane frequency. Since the process is stochastic, your statements will be given in terms of probabilities (see Chapter 7). For example, the probability of ĥ hurricanes occurring over the next T years (e.g., 1, 5, 20, etc.) is . . . f (ĥ |λ,T) = exp(−λT) (λT)h/h! for h = 0,1,. . . , λ>0, and T > 0 (12.1) . . . The hat notation is used to indicate future values. The parameter λ and statistic T appear in the formula as a product, which is the mean and variance of the distribution. Knowledge about λ can come from historical written archives and instrumental records. It is logical for you to want to use as much of this information as possible before inferring something about future activity. This requires you to treat λ as a parameter that can be any positive real number, rather than as a fixed constant. One form for expressing your judgment about the values λ can take is through the gamma distribution.
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Arı, Yakup. "COGARCH Models." In Emerging Applications of Differential Equations and Game Theory, 79–97. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-0134-4.ch005.

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In this chapter, the features of a continuous time GARCH (COGARCH) process is discussed since the process can be applied as an explicit solution for the stochastic differential equation which is defined for the volatility of unequally spaced time series. COGARCH process driven by a Lévy process is an analogue of discrete time GARCH process and is further generalized to solutions of Lévy driven stochastic differential equations. The Compound Poisson and Variance Gamma processes are defined and used to derive the increments for the COGARCH process. Although there are various parameter estimation methods introduced for COGARCH, this study is focused on two methods which are Pseudo Maximum Likelihood Method and General Methods of Moments. Furthermore, an example is given to illustrate the findings.
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"Appendices B: Asymptotic Variance Formulas, Gamma Functions, and Order Statistics." In Statistical Models and Methods for Lifetime Data, 539–43. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2011. http://dx.doi.org/10.1002/9781118033005.app2.

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Koumaras, Harilaos, Charalampos Skianis, and Anastasios Kourtis. "Analysis and Modeling of H.264 Unconstrained VBR Video Traffic." In Innovations in Mobile Multimedia Communications and Applications, 227–43. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-60960-563-6.ch016.

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In future communication networks, video is expected to represent a large portion of the total traffic, given that especially variable bit rate (VBR) coded video streams, are becoming increasingly popular. Consequently, traffic modeling and characterization of such video services is essential for the efficient traffic control and resource management. Besides, providing an insight of video coding mechanisms, traffic models can be used as a tool for the allocation of network resources, the design of efficient networks for streaming services and the reassurance of specific QoS characteristics to the end users. The new H.264/AVC standard, proposed by the ITU-T Video Coding Expert Group (VCEG) and ISO/IEC Moving Pictures Expert Group (MPEG), is expected to dominate in upcoming multimedia services, due to the fact that it outperforms in many fields the previous encoded standards. This article presents both a frame and a layer (i.e. I, P and B frames) level analysis of H.264 encoded sources. Analysis of the data suggests that the video traffic can be considered as a stationary stochastic process with an autocorrelation function of exponentially fast decay and a marginal frame size distribution of approximately Gamma form. Finally, based on the statistical analysis, an efficient model of H.264 video traffic is proposed.
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Conference papers on the topic "Variance Gamma Model"

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Yuxian Zheng, Ming Lu, Jinping Yu, and Xiaofeng Yang. "Notice of Retraction: Convertible bond pricing based on Variance Gamma model." In 2010 3rd IEEE International Conference on Computer Science and Information Technology (ICCSIT 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccsit.2010.5565114.

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Yu, Jinping, Xiaofeng Yang, Shenghong Li, and Xiaohu Yang. "Pricing Convertible Bond with Call Clause in Exponential Variance Gamma Model." In 2009 International Conference on Business Intelligence and Financial Engineering (BIFE). IEEE, 2009. http://dx.doi.org/10.1109/bife.2009.156.

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Yang, Xiaofeng, Jinping Yu, Shenghong Li, and Albert Jerry Cristoforo. "Notice of Retraction: The PIDE pricing model of interest rate swap with default risk under Variance Gamma process." In 2010 3rd IEEE International Conference on Computer Science and Information Technology (ICCSIT 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccsit.2010.5564827.

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LeCompte, Brian, Tosin Majekodunmi, Mike Staines, Gareth Taylor, Barry Zhang, Randy Evans, and Nathan Chang. "Machine Learning Prediction of Formation Evaluation Logs in the Gulf of Mexico." In Offshore Technology Conference. OTC, 2021. http://dx.doi.org/10.4043/31093-ms.

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Abstract The objective of the paper is to describe the application of artificial intelligence software to predict formation evaluation logs (compressional sonic, shear sonic and density) using only gamma ray, and resistivity log data and drilling dynamics data as received by the electronic drilling recorder (EDR). The software was applied real-time as a well was being drilled in deepwater Gulf of Mexico. Thorough examination and conditioning of EDR and wireline data give way to a training model construction for the artificial neural network (ANN) using full suites of log-data in offset wells. Next, a neural network architecture and associated hyperparameters are chosen and tested. The fully trained and validated model is applied to the gamma ray, resistivity and EDR of the target well while drilling. Real-time EDR and wireline data flow via WITSML from rig to cloud and data is delivered to the client. The results of the study indicate the simulated log data were comparable to those measured from conventional logging tools over the study area. In both blind well tests the density agreed with the conventional log results within 1.1 % and the compressional within 2.51 % (Figure 1). Each of these is well within the range of variance expected of repeat runs of a conventional logging tool. A primary driver for near real-time logs was to confirm structural depth of the target sands along the well bore. There was a depleted sand below the expected TD of the well that, if encountered, could have led to total losses and possible loss of the wellbore. It was critical to have real-time logs to characterize the sands above the depleted sand, using every possible petrophysical and geologic character to refine the log correlation. This integration of all the logs provided the best interpretation of the sand quality and led toward the completion decision. AI-based logs are a highly cost-effective alternative to LWD logging. It presents an environmentally friendly approach as there is no logging personnel on-site and no expensive and potentially dangerous nuclear sources in the hole The deployment of this patented, machine learning-driven, real-time simulation of formation evaluation logs is unique in using only gamma ray, resistivity and drilling data. It is particularly useful in the overburden section where formation evaluation tools are often not run for cost reasons, in side-tracks, in HP/HT settings and operational risk mitigation. It provides additive data for other petrophysical/QI/rock property analyses including seismic inversion, shale content, porosity, log QC/editing, real-time LWD, drilling optimization, etc.
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Popescu, M. "Improved direct and inverse gamma models for vector controlled induction machines." In 8th International Conference on Power Electronics and Variable Speed Drives. IEE, 2000. http://dx.doi.org/10.1049/cp:20000236.

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Becherini, Y., M. Punch, and H.E.S.S. Collaboration. "Performance of HESS-II in multi-telescope mode with a multi-variate analysis." In HIGH ENERGY GAMMA-RAY ASTRONOMY: 5th International Meeting on High Energy Gamma-Ray Astronomy. AIP, 2012. http://dx.doi.org/10.1063/1.4772366.

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Sandhu, Jatinder Pal Singh. "Local-Correlation Based Zero-Equation Transition Model for Turbomachinery." In ASME 2019 Gas Turbine India Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gtindia2019-2615.

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Abstract In this paper, we present a new local-correlation based zero-equation transition model. The new model, which is derived from the local-correlation based one-equation gamma transition model (Menter, F. R., Smirnov, P. E., Liu, T., and Avancha, R., A One-Equation Local Correlation-Based Transition Model, Flow, Turbulence and Combustion, vol. 95, 2015, pp. 583619.), does not require any additional equation to be solved, by defining a new variable, which captures the turbulent kinetic energy and intermittency collectively. The new model only adds three more source terms to the existing transport equation of turbulent kinetic energy. Hence the new model is straightforward to implement in already existing RANS solvers and reduces the computational memory requirement as compared to the other transition models. The transition prediction capability of the new model is tested and compared against the one-equation gamma transition model, especially for turbomachinery applications, where bypass transition is the primary transition mechanism, using a standard flat plate test case, and S809 airfoil. Preliminary results show that the new zero-equation transition model produces satisfactory results in terms of transition-location prediction.
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Ichimasa, Ryotaro, Ann Thushari, and Masa-aki Hashimoto. "Constraints from Supernovae and Gamma-ray Bursts on the Variable Dark Energy Density Model." In Proceedings of the 14th International Symposium on Nuclei in the Cosmos (NIC2016). Journal of the Physical Society of Japan, 2017. http://dx.doi.org/10.7566/jpscp.14.020107.

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Browarczyk, Maciej, Renata Kalicka, and Seweryn Lipiński. "Proposal of New Tracer Concentration Model in Lung PCT Study - Comparison with Commonly Used Gamma-variate Model." In 10th International Conference on Bio-inspired Systems and Signal Processing. SCITEPRESS - Science and Technology Publications, 2017. http://dx.doi.org/10.5220/0006115101340140.

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Yan, Meichen, Bo Sun, Zhifeng Li, Dezhen Yang, Tianyuan Ye, Jinghua Yao, and Mumeng Wei. "An improved time-variant reliability method for structural components based on gamma degradation process model." In 2016 Prognostics and System Health Management Conference (PHM-Chengdu). IEEE, 2016. http://dx.doi.org/10.1109/phm.2016.7819808.

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