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Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Probability mass functions"

Gilbert, L., G. de Cooman, and E. E. Kerre. "Practical implementation of possibilistic probability mass functions." Soft Computing - A Fusion of Foundations, Methodologies and Applications 7, no. 5 (April 1, 2003): 304–9. http://dx.doi.org/10.1007/s00500-002-0217-3.

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Racine, Jeffrey S., Qi Li, and Karen X. Yan. "Kernel smoothed probability mass functions for ordered datatypes." Journal of Nonparametric Statistics 32, no. 3 (May 12, 2020): 563–86. http://dx.doi.org/10.1080/10485252.2020.1759595.

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Drane, J. Wanzer, Suhua Cao, Lixia Wang, and T. Postelnicu. "Limiting Forms of Probability Mass Functions via Recurrence Formulas." American Statistician 47, no. 4 (November 1993): 269. http://dx.doi.org/10.2307/2685285.

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Drane, J. Wanzer, Suhua Cao, Lixia Wang, and T. Postelnicu. "Limiting forms of Probability Mass Functions via Recurrence Formulas." American Statistician 47, no. 4 (November 1993): 269–74. http://dx.doi.org/10.1080/00031305.1993.10475996.

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Bergbusch, Peter A. "Isochrone Probability Functions for Old Stellar Systems." Symposium - International Astronomical Union 190 (1999): 345–46. http://dx.doi.org/10.1017/s0074180900118170.

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The isochrone probability function (IPF) is derived from the slope of the mass–distance relation on an isochrone in where the distance along the isochrone is computed with respect to some arbitrary, well-defined point. IPFs contain the information needed to calculate both luminosity functions and color functions, and they provide a straightforward way of generating synthetic stellar populations.

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Provost, Serge B., Min Jiang, and Hyung-Tae Ha. "Moment-Based Approximations of Probability Mass Functions with Applications Involving Order Statistics." Communications in Statistics - Theory and Methods 38, no. 12 (June 3, 2009): 1969–81. http://dx.doi.org/10.1080/03610920902835052.

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Warr, Richard L. "Numerical Approximation of Probability Mass Functions via the Inverse Discrete Fourier Transform." Methodology and Computing in Applied Probability 16, no. 4 (August 24, 2013): 1025–38. http://dx.doi.org/10.1007/s11009-013-9366-3.

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Rachev, S. T., and I. Olkin. "Mass transportation problems with capacity constraints." Journal of Applied Probability 36, no. 2 (June 1999): 433–45. http://dx.doi.org/10.1239/jap/1032374463.

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We exhibit solutions of Monge–Kantorovich mass transportation problems with constraints on the support of the feasible transportation plans and additional capacity restrictions. The Hoeffding–Fréchet inequalities are extended for bivariate distribution functions having fixed marginal distributions and satisfying additional constraints. Sharp bounds for different probabilistic functionals (e.g. Lp-distances, covariances, etc.) are given when the family of joint distribution functions has prescribed marginal distributions, satisfies restrictions on the support, and is bounded from above, or below, by other distributions.

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Wang, Jiandong, Zhen Wang, Xuan Zhou, and Fan Yang. "Design of delay timers based on estimated probability mass functions of alarm durations." Journal of Process Control 110 (February 2022): 154–65. http://dx.doi.org/10.1016/j.jprocont.2022.01.002.

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Belaid, Nawal, Smail Adjabi, Nabil Zougab, and Célestin C. Kokonendji. "Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions." Journal of the Korean Statistical Society 45, no. 4 (December 2016): 557–67. http://dx.doi.org/10.1016/j.jkss.2016.04.001.

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Дисертації з теми "Probability mass functions"

Bayramoglu, Muhammet Fatih. "The Hilbert Space Of Probability Mass Functions And Applications On Probabilistic Inference." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613613/index.pdf.

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The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by using the tools provided by the Hilbert space of pmfs. The resulting factorization is special for two reasons. First, it reveals the algebraic relations between the involved random variables. Second, it determines the conditional independence relations between the random variables. Due to the first property of the resulting factorization, it can be shown that channel decoders can be employed in the solution of probabilistic inference problems other than decoding. This approach might lead to new probabilistic inference algorithms and new hardware options for the implementation of these algorithms. An example of new inference algorithms inspired by the idea of using channel decoder for other inference tasks is a multiple-input multiple-output (MIMO) detection algorithm which has a complexity of the square-root of the optimum MIMO detection algorithm. Keywords: The Hilbert space of pmfs, factorization of pmfs, probabilistic inference, MIMO detection, Markov random fields iv

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Kharoufeh, Jeffrey P. "Density estimation for functions of correlated random variables." Ohio : Ohio University, 1997. http://www.ohiolink.edu/etd/view.cgi?ohiou1177097417.

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Pfister, Mark. "Distribution of a Sum of Random Variables when the Sample Size is a Poisson Distribution." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3459.

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A probability distribution is a statistical function that describes the probability of possible outcomes in an experiment or occurrence. There are many different probability distributions that give the probability of an event happening, given some sample size n. An important question in statistics is to determine the distribution of the sum of independent random variables when the sample size n is fixed. For example, it is known that the sum of n independent Bernoulli random variables with success probability p is a Binomial distribution with parameters n and p: However, this is not true when the sample size is not fixed but a random variable. The goal of this thesis is to determine the distribution of the sum of independent random variables when the sample size is randomly distributed as a Poisson distribution. We will also discuss the mean and the variance of this unconditional distribution.

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Green, Christopher Lee. "IP Algorithm Applied to Proteomics Data." Diss., CLICK HERE for online access, 2004. http://contentdm.lib.byu.edu/ETD/image/etd618.pdf.

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Gomez, Beltran Liseth Ana Délia. "A interação entre a fertilidade do solo e a massa da semente influencia os atributos funcionais de espécies arbóreas tropicais?" Universidade Federal de São Carlos, 2017. https://repositorio.ufscar.br/handle/ufscar/9380.

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Biological, physical and chemical characteristics of the soil are environmental filters that strongly influence the composition of the plant communities. The knowledge of the effect of soil conditions on the survival and growth of plant species is important for the recovery activities in degraded areas. These aspects of plant performance are directly related to the functional characteristics of species, so understanding the responses of the different resources to different soil conditions can help to choose species that are best suited to each area. We have carried out an experiment in nursery with the objective of evaluating the influence of different soil treatments on survival and functional characteristics; Leaf Area (LA), Specific Leaf Area (SLA), Leaf Dry Matter Content (LDMC), Root Mass Fraction (RMF), Specific Root Length (SRL) and Relative Height Increment (RHI) of eleven native forest species forming a seed mass gradient. The treatments used in the experiment were control soil - without the addition of any fertilizer (CT); addition of chemical fertilizer - NPK (QU); addition of organic fertilizer (OR) and the addition of chemical fertilizer and organic fertilizer (OQ). Soil chemical attributes in the four treatments were evaluated after two and seven months after planting to verify the changes that occurred over time. In addition, we evaluated soil chemical attributes of natural areas of occurrence of these species, preserved and degraded forests. The monitoring of the experiment was performed for four months and at the end of this period we recorded survival and measured the functional characteristics of all species. Chemical soil attributes used in the treatments CT and QU were more similar to the attributes of the areas used as reference, showing higher values of acidity potential (H + Al) and cation exchange capacity (CTC), and lower values of nitrogen (N) and organic matter. The seed mass heavily influenced survival in CT, QU and OR treatments and did not differed between CT and QU treatments and, furthermore, in OR treatment the survival was greater than in CT and QU treatments. The effect of seed mass on survival was not significant in OQ treatment. We detected a high positive correlation between SLA, RMF and SRL that were negatively correlated with LA and RHI. The functional properties of the species differed between treatments, but no differences were detected between treatments OR and OQ. In these two treatments, species reached higher values of LA and RHI and lower values of SRL, RMF and SLA than other treatments. Functional attributes varied between and within species. Phenotypic plasticity was higher in LA, RHI, SRL and RMF, and the variation of LA, RHI and SRL were highly correlated with each other and together were negatively related to seed mass. This study showed that limited terrestrial resources were able to modify root 12 architecture, leaf traits and the rate of growth of the aerial parts, which suggests that plants should invest more in fundraising bodies to increase the chances of survival. Intra-specific variation of LA, RHI, SRL, RHI and LDMC characteristics were correlated with each other and negatively correlated with seed mass. Smaller seed species were more plastic than larger seed species. In the treatment CT, these species reached higher values of SLA and SRL, while treatments with organic matter addition, these species reach higher values of LA and RHI. The addition of organic matter in the soil increased the survival and growth of plants, in particular small seed species. Thus, the addition of organic matter as pre-planting treatment proved to be more efficient to increase the performance of native tree species. However, experiments under field conditions are necessary to quantify the efficacy of manure on the reintroduction of native species into deforested forests.
As características biológicas, físicas e químicas do solo são filtros ambientais que influenciam fortemente a composição de comunidades vegetais. O conhecimento do efeito das condições do solo na sobrevivência e no crescimento de espécies vegetais é de grande importância para atividades de recuperação de áreas degradadas. Tais aspectos do desempenho de plantas estão diretamente relacionados aos traços funcionais das espécies, consequentemente a compreensão das respostas dos diferentes traços a diferentes condições edáficas pode auxiliar na escolha de espécies que se adaptem melhor a cada área. Nós conduzimos um experimento em viveiro com o objetivo de avaliar a influência de diferentes tratamentos de solo na sobrevivência e nos traços funcionais; Área Foliar (AF), Área foliar específica (AFE), Conteúdo de matéria seca foliar (CMSF) Fração da massa da raiz (FMR), Comprimentos especifico da raiz (CER) e Taxa de crescimento em altura (TCA) de onze espécies florestais nativas que formam um gradiente de massa de semente. Os tratamentos usados no experimento foram: solo controle – sem a adição de nenhum tipo de adubo ou fertilizante (CT); adição de fertilizante químico - NPK (QU); adição de adubo orgânico (OR) e adição fertilizante químico e de adubo orgânico (OQ). Os atributos químicos do solo nos quatro tratamentos foram avaliados após dois e sete meses da semeadura para verificar as mudanças ocorridas ao longo do tempo. Além disto, avaliamos os atributos químicos do solo de áreas naturais de ocorrência destas espécies, florestas preservadas e degradadas. O monitoramento do experimento foi conduzido por quatro meses e ao final deste período registramos a sobrevivência e as medidas dos traços funcionais de todas as espécies. Os atributos químicos dos solos usados nos tratamentos Controle e Químico foram mais semelhantes aos atributos das áreas usadas como referência, apresentando maiores valores de acidez potencial (H+Al) e Capacidade de troca catiônica (CTC), e menores valores de Nitrogênio (N) e de matéria orgânica. A massa da semente influenciou fortemente a sobrevivência nos tratamentos CT, QU e OR, e não diferiu entre os tratamentos CT e QU, por outro lado, no tratamento OR a sobrevivência foi maior em comparação com os tratamentos CT e QU. O efeito da massa da semente na sobrevivência não foi significativo no tratamento OQ. Detectamos uma alta correlação positiva entre os traços AFE, FMR e CER que foram negativamente correlacionados com AF e TCA. Os atributos funcionais das espécies diferiram entre os tratamentos, porém não foram detectadas diferenças entre os tratamentos OR e OQ. Nestes dois tratamentos as espécies alcançaram valores mais altos de AF e TCA e valores de 8 CER, FMR e AFE mais baixos do que nos demais tratamentos. Os atributos funcionais variaram entre e dentro de espécies. A plasticidade fenotípica foi maior com relação a AF, TCA, CER e FMR, sendo que a variação de AF, TCA e CER foram altamente correlacionadas entre si e juntas foram negativamente relacionadas com a massa da semente. Este estudo mostrou que a limitação de recursos do solo foi capaz de modificar a arquitetura das raízes, os traços foliares e a taxa de crescimento das partes aéreas, sugerindo que plantas devem investir mais em órgãos de captação de recursos para aumentar as chances de sobrevivência. A variação intraespecífica dos traços AF, TCA, AFE, CER e CMSF foram correlacionados entre si e negativamente correlacionados com a massa da semente. Espécies de sementes menores foram mais plásticas do que espécies de sementes maiores. No tratamento CT estas espécies alcançaram maiores valores de AFE e CER, enquanto que nos tratamentos que receberam adição de matéria orgânica, estas espécies alcançaram maiores valores de AF e TCR. A adição de matéria orgânica ao solo aumentou a sobrevivência e o crescimento das plantas, especialmente das espécies de sementes menores. Nesse sentido, a adição de matéria orgânica como tratamento pré-plantio mostrou ser mais eficiente para aumentar o desempenho de espécies arbóreas nativas. No entanto experimentos sob condições de campo são necessários para quantificar a eficácia do uso de esterco na reintrodução de espécies nativa em florestas desmatadas.

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Somé, Sobom Matthieu. "Estimations non paramétriques par noyaux associés multivariés et applications." Thesis, Besançon, 2015. http://www.theses.fr/2015BESA2030/document.

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Dans ce travail, l'approche non-paramétrique par noyaux associés mixtes multivariés est présentée pour les fonctions de densités, de masse de probabilité et de régressions à supports partiellement ou totalement discrets et continus. Pour cela, quelques aspects essentiels des notions d'estimation par noyaux continus (dits classiques) multivariés et par noyaux associés univariés (discrets et continus) sont d'abord rappelés. Les problèmes de supports sont alors révisés ainsi qu'une résolution des effets de bords dans les cas des noyaux associés univariés. Le noyau associé multivarié est ensuite défini et une méthode de leur construction dite mode-dispersion multivarié est proposée. Il s'ensuit une illustration dans le cas continu utilisant le noyau bêta bivarié avec ou sans structure de corrélation de type Sarmanov. Les propriétés des estimateurs telles que les biais, les variances et les erreurs quadratiques moyennes sont également étudiées. Un algorithme de réduction du biais est alors proposé et illustré sur ce même noyau avec structure de corrélation. Des études par simulations et applications avec le noyau bêta bivarié avec structure de corrélation sont aussi présentées. Trois formes de matrices des fenêtres, à savoir, pleine, Scott et diagonale, y sont utilisées puis leurs performances relatives sont discutées. De plus, des noyaux associés multiples ont été efficaces dans le cadre de l'analyse discriminante. Pour cela, on a utilisé les noyaux univariés binomial, catégoriel, triangulaire discret, gamma et bêta. Par la suite, les noyaux associés avec ou sans structure de corrélation ont été étudiés dans le cadre de la régression multiple. En plus des noyaux univariés ci-dessus, les noyaux bivariés avec ou sans structure de corrélation ont été aussi pris en compte. Les études par simulations montrent l'importance et les bonnes performances du choix des noyaux associés multivariés à matrice de lissage pleine ou diagonale. Puis, les noyaux associés continus et discrets sont combinés pour définir les noyaux associés mixtes univariés. Les travaux ont aussi donné lieu à la création d'un package R pour l'estimation de fonctions univariés de densités, de masse de probabilité et de régression. Plusieurs méthodes de sélections de fenêtres optimales y sont implémentées avec une interface facile d'utilisation. Tout au long de ce travail, la sélection des matrices de lissage se fait généralement par validation croisée et parfois par les méthodes bayésiennes. Enfin, des compléments sur les constantes de normalisations des estimateurs à noyaux associés des fonctions de densité et de masse de probabilité sont présentés
This work is about nonparametric approach using multivariate mixed associated kernels for densities, probability mass functions and regressions estimation having supports partially or totally discrete and continuous. Some key aspects of kernel estimation using multivariate continuous (classical) and (discrete and continuous) univariate associated kernels are recalled. Problem of supports are also revised as well as a resolution of boundary effects for univariate associated kernels. The multivariate associated kernel is then defined and a construction by multivariate mode-dispersion method is provided. This leads to an illustration on the bivariate beta kernel with Sarmanov's correlation structure in continuous case. Properties of these estimators are studied, such as the bias, variances and mean squared errors. An algorithm for reducing the bias is proposed and illustrated on this bivariate beta kernel. Simulations studies and applications are then performed with bivariate beta kernel. Three types of bandwidth matrices, namely, full, Scott and diagonal are used. Furthermore, appropriated multiple associated kernels are used in a practical discriminant analysis task. These are the binomial, categorical, discrete triangular, gamma and beta. Thereafter, associated kernels with or without correlation structure are used in multiple regression. In addition to the previous univariate associated kernels, bivariate beta kernels with or without correlation structure are taken into account. Simulations studies show the performance of the choice of associated kernels with full or diagonal bandwidth matrices. Then, (discrete and continuous) associated kernels are combined to define mixed univariate associated kernels. Using the tools of unification of discrete and continuous analysis, the properties of the mixed associated kernel estimators are shown. This is followed by an R package, created in univariate case, for densities, probability mass functions and regressions estimations. Several smoothing parameter selections are implemented via an easy-to-use interface. Throughout the paper, bandwidth matrix selections are generally obtained using cross-validation and sometimes Bayesian methods. Finally, some additionnal informations on normalizing constants of associated kernel estimators are presented for densities or probability mass functions

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Bailey, Lara. "Deformable Registration to Create Cytoarchitectonic Probability Maps for Functional Analysis of Primary Auditory Cortex." Thesis, 2008. http://hdl.handle.net/1974/1536.

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A novel method is presented for analyzing fMRI data, which relies on probabilistic estimates of microanatomically defined regions in individual fMRI volunteers. Postmortem structural and cytoarchitectonic information from the Julich/Dusseldorf group in Germany is aligned to the high-resolution structural MR images of functional MRI volunteers. This is achieved using nonlinear registration, which is applied only to the region of interest. The registered postmortem datasets are then combined into probability maps for microanatomically defined regions that are tailored to the anatomy of individual fMRI volunteers. These are then used as weighted spatial filters on functional MR data. In this thesis, three regions of the primary auditory cortex (located on Heschl's gyrus) have been targeted, and the analysis method is used to explore how these three areas respond to different kinds of sound. Regions Te1.0 and Te1.2 both demonstrate pitch sensitivity, consistent with published observations of the functional response of homologous regions in nonhuman primates. Area Te1.1 displayed sensitivity to both noise and pitch, consistent with the theory that it is homologous with the microanatomically similar area CM in nonhuman primates. Furthermore, the custom probability maps are much less diffuse and anatomically more precise than previous versions generated using the same postmortem data, and therefore permit a more sensitive and anatomically precise analysis of functional activity. This method could be applied to any other microanatomically defined region that has been characterized in the Julich postmortem dataset.
Thesis (Master, Computing) -- Queen's University, 2008-09-26 19:50:54.582

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Книги з теми "Probability mass functions"

Sharma, Megha. Computing the probability mass function of the maximum flow through a reliable network. Ahmedabad: Indian Institute of Management, 2009.

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Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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Horing, Norman J. Morgenstern. Retarded Green’s Functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0005.

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Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, which represent the time development of one (or a few) state(s) that may be understood as localized but are in interaction with a continuum of states, are discussed and applied to chemisorption. Introductions are also made to the Dyson integral equation, T-matrix and the Dirac delta-function potential, with the latter applied to random impurity scattering. The retarded Green’s function in the presence of random impurity scattering is exhibited in the Born and self-consistent Born approximations, with application to Ando’s semi-elliptic density of states for the 2D Landau-quantized electron-impurity system. Important retarded Green’s functions and their methods of derivation are discussed. These include Green’s functions for electrons in magnetic fields in both three dimensions and two dimensions, also a Hamilton equation-of-motion method for the determination of Green’s functions with application to a 2D saddle potential in a time-dependent electric field. Moreover, separable Hamiltonians and their product Green’s functions are discussed with application to a one-dimensional superlattice in axial electric and magnetic fields. Green’s function matching/joining techniques are introduced and applied to spatially varying mass (heterostructures) and non-local electrostatics (surface plasmons).

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Hall, Peter. Principal component analysis for functional data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.8.

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This article discusses the methodology and theory of principal component analysis (PCA) for functional data. It first provides an overview of PCA in the context of finite-dimensional data and infinite-dimensional data, focusing on functional linear regression, before considering the applications of PCA for functional data analysis, principally in cases of dimension reduction. It then describes adaptive methods for prediction and weighted least squares in functional linear regression. It also examines the role of principal components in the assessment of density for functional data, showing how principal component functions are linked to the amount of probability mass contained in a small ball around a given, fixed function, and how this property can be used to define a simple, easily estimable density surrogate. The article concludes by explaining the use of PCA for estimating log-density.

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VanMarcke, E. H. Quantum Origins of Cosmic Structure: Probability Density Function of Quantity-mass-ratio Logarithm. Swets & Zeitlinger Publishers, 1997.

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Information-Theoretic Methods for Estimating of Complicated Probability Distributions, Volume 207 (Mathematics in Science and Engineering). Elsevier Science, 2006.

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Частини книг з теми "Probability mass functions"

Kay, Steven M. "Conditional Probability Mass Functions." In Intuitive Probability and Random Processes Using MATLAB®, 215–46. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/0-387-24158-2_8.

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Yi, Pu, Hao Wang, Tao Xie, Darko Marinov, and Wing Lam. "A Theoretical Analysis of Random Regression Test Prioritization." In Tools and Algorithms for the Construction and Analysis of Systems, 217–35. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99527-0_12.

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AbstractRegression testing is an important activity to check software changes by running the tests in a test suite to inform the developers whether the changes lead to test failures. Regression test prioritization (RTP) aims to inform the developers faster by ordering the test suite so that tests likely to fail are run earlier. Many RTP techniques have been proposed and are often compared with the random RTP baseline by sampling some of the n! different test-suite orders for a test suite with n tests. However, there is no theoretical analysis of random RTP. We present such an analysis, deriving probability mass functions and expected values for metrics and scenarios commonly used in RTP research. Using our analysis, we revisit some of the most highly cited RTP papers and find that some presented results may be due to insufficient sampling. Future RTP research can leverage our analysis and need not use random sampling but can use our simple formulas or algorithms to more precisely compare with random RTP.

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Kutílek, Miroslav, Miroslav Krejca, and Jana Kupcová-Vlašimská. "The role of estimation error in probability density function of soil hydraulic parameters: Pedotop scale." In Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere, 259–63. Washington, D. C.: American Geophysical Union, 2002. http://dx.doi.org/10.1029/129gm21.

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Jenny, Patrick, and Daniel W. Meyer. "Transported Probability and Mass Density Function (PDF/MDF) Methods for Uncertainty Assessment and Multi-Scale Problems." In Lecture Notes in Computational Science and Engineering, 35–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22061-6_2.

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Liu, Hang, Yuyin Ma, Peng Chen, Yunni Xia, Yong Ma, Wanbo Zheng, and Xiaobo Li. "Scheduling Multi-workflows over Edge Computing Resources with Time-Varying Performance, A Novel Probability-Mass Function and DQN-Based Approach." In Web Services – ICWS 2020, 197–209. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-59618-7_13.

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Csenki, Attila. "The Number of Visits to a Subset of the State Space by an Irreducible Semi-Markov Process during a Finite Time Interval: The Probability Mass Function." In Dependability for Systems with a Partitioned State Space, 179–204. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-2674-1_10.

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Donovan, Therese M., and Ruth M. Mickey. "Probability Mass Functions." In Bayesian Statistics for Beginners, 87–107. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198841296.003.0008.

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This chapter focuses on probability mass functions. One of the primary uses of Bayesian inference is to estimate parameters. To do so, it is necessary to first build a good understanding of probability distributions. This chapter introduces the idea of a random variable and presents general concepts associated with probability distributions for discrete random variables. It starts off by discussing the concept of a function and goes on to describe how a random variable is a type of function. The binomial distribution and the Bernoulli distribution are then used as examples of the probability mass functions (pmf’s). The pmfs can be used to specify prior distributions, likelihoods, likelihood profiles and/or posterior distributions in Bayesian inference.

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Trappenberg, Thomas P. "Basic probability theory." In Fundamentals of Machine Learning, 121–40. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198828044.003.0006.

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The discussion provides a refresher of probability theory, in particular with respect to the formulations that build the theoretical language of modern machine learning. Probability theory is the formalism of random numbers, and this chapter outlines what these are and how they are characterized by probability density or probability mass functions. How such functions have traditionally been characterized is covered, and a review of how to work with such mathematical objects such as transforming density functions and how to measure differences between density function is presented. Definitions and basic operations with multiple random variables, including the Bayes law, are covered. The chapter ends with an outline of some important approximation techniques of so-called Monte Carlo methods.

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Edge, M. D. "Probability and random variables." In Statistical Thinking from Scratch, 38–59. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198827627.003.0005.

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This chapter considers the rules of probability. Probabilities are non-negative, they sum to one, and the probability that either of two mutually exclusive events occurs is the sum of the probability of the two events. Two events are said to be independent if the probability that they both occur is the product of the probabilities that each event occurs. Bayes’ theorem is used to update probabilities on the basis of new information, and it is shown that the conditional probabilities P(A|B) and P(B|A) are not the same. Finally, the chapter discusses ways in which distributions of random variables can be described, using probability mass functions for discrete random variables and probability density functions for continuous random variables.

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Essington, Timothy E. "Random Variables and Probability." In Introduction to Quantitative Ecology, 109–24. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192843470.003.0007.

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The chapter “Random Variables and Probability” serves as both a review and a reference on probability. The random variable is the core concept in understanding probability, parameter estimation, and model selection. This chapter reviews the basic idea of a random variable and discusses the two main kinds of random variables: discrete random variables and continuous random variables. It covers the distinction between discrete and continuous random variables and outlines the most common probability mass or density functions used in ecology. Advanced sections cover distributions such as the gamma distribution, Student’s t-distribution, the beta distribution, the beta-binomial distribution, and zero-inflated models.

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Тези доповідей конференцій з теми "Probability mass functions"

Tan, Choon Peng, Sin Yen Chu, and Wei Yeing Pan. "Finite-order universal portfolios generated by probability mass functions." In INTERNATIONAL CONFERENCE ON MATHEMATICS, ENGINEERING AND INDUSTRIAL APPLICATIONS 2014 (ICoMEIA 2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4915655.

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Bayramoglu, Muhammet Fatih, and Ali Ozgur Yilmaz. "Factorization of joint probability mass functions into parity check interactions." In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5205262.

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Manickam, Shivkumar K. "Probability Mass Functions for which Sources have the Maximum Minimum Expected Length." In 2019 National Conference on Communications (NCC). IEEE, 2019. http://dx.doi.org/10.1109/ncc.2019.8732264.

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Li, Hewenxuan, and David Chelidze. "Identification of Variable Amplitude Fatigue Loading Based on Bivariate Probability Mass Functions." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97488.

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Abstract Fatigue life estimation under variable amplitude (VA) loading remains one of the major unresolved engineering problems. When engineering structures experience VA loading, the corresponding load at the crack front will be highly non-stationary. Under such conditions, the load interaction effects greatly affect fatigue crack propagation rate and can cause significant variation in the corresponding fatigue life. Existing characterization methods focus on single overload effect and their extensions to sequence of overloads which does not reflect the irregularity of the realistic loading. In this paper, numerical simulations were used to compare the fatigue life under various synthetic load time histories. The resulting time to failure estimation, concerning statistically and spectrally identical deterministic loads and their stochastic surrogates, exhibits drastic difference which reflects the corresponding differences in the temporal structure of the loads, which are not differentiated by their linear characteristics. This indicates that the temporal dynamics of the load time histories have considerable influence on fatigue crack propagation and fracture. In order to differentiate temporal dynamics of the synthetic loading, new bivariate probability mass functions (BPMFs) are proposed. They can capture and preserve the underlying temporal dynamics of locally non-stationary variable amplitude load-time histories with identical linear statistics. And qualitative explanations of the potential of this proposed method for fatigue life estimation under VA loading are discussed.

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Fatih Bayramoglu, Muhammet, and Ali Ozgur Yilmaz. "A Hilbert space of probability mass functions and applications on the sum-product algorithm." In 2008 5th International Symposium on Turbo Codes and Related Topics. IEEE, 2008. http://dx.doi.org/10.1109/turbocoding.2008.4658722.

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Wong, Chun Nam, Hong-Zhong Huang, Jingqi Xiong, and Tianyou Hu. "Weibull Distributed Stress-Dependent Strength Analysis of Aeroengine Alloy Using Lagrange Factor Polynomial." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28090.

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In this paper, the unilateral dependency of strength on stress is taken into account. And the stress-dependent strength is represented by a discrete random variable that has different conditional probability mass functions under different stress amplitudes. Then the Lagrange factor polynomial technique is developed to generate the stress-strength interference model with stress-dependent strength. This model assumes that the strength probability mass function is Weibull distributed, while the stress probability mass function is Normal distributed. Accuracy of this method is investigated by an aeroengine bearing cage alloy. Structural reliabilities are computed as 0.796 to 0.986 under several operation modes, which are analyzed by varying the Weibull shape parameter from 1 to 6. Then probability mean function estimated by Lagrange factor polynomial has relatively low errors over most span of the stress dependent strength distribution. With this approach stress-dependent strength reliability of aeroengine structural systems can be established conveniently. Meanwhile the application range of the classical stress-strength interference model can be extended.

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Jeong, D. Y. "Probabilistic Approach to Conditional Probability of Release of Hazardous Materials From Railroad Tank Cars During Accidents." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10872.

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This paper describes a probabilistic approach to estimate the conditional probability of release of hazardous materials from railroad tank cars during train accidents. Monte Carlo methods are used in developing a probabilistic model to simulate head impacts. The model is based on the physics of impact in conjunction with assumptions regarding the probability distribution functions of the various factors that affect the loss of lading. These factors include impact velocity, indenter size, tank material, tank diameter, effective collision mass, and tank thickness. Moreover, each factor is treated as a random variable characterized by its assumed distribution function, mean value, and standard deviation (or variance). Reverse engineering is performed to back-calculate the mean values and standard deviations of these random variables that reproduce trends observed in available accident data. The calibrated model is then used to conduct a probabilistic sensitivity analysis to examine the relative effect of these factors on the conditional probability of release. Results from the probabilistic sensitivity analysis indicate that the most significant factors that affect conditional probability of release are impact velocity, effective collision mass, and indenter size.

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Ward, Nicholas J., Stephen Ekwaro-Osire, and João Paulo Dias. "Uncertainty Quantification of Mass and Aerodynamic Rotor Imbalance for Offshore Wind Turbines." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-15792.

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Abstract One promising way to address turbine durability issues is early detection of mass and aerodynamic imbalances. More probabilistic methods are necessary to improve the accuracy of rotor imbalance diagnostics. The research question that this work addresses is: can current imbalance detection for an offshore wind turbine be improved through uncertainty quantification of its operating conditions? An uncertainty quantification strategy was proposed to model uncertainties in wind speed, pitch angle, and blade mass density using assumed probability density functions based on available data/information. These input parameters served as random variables that were fed into an aeroelastic software to model dynamic and power output variables for multiple imbalance scenarios. 4% variation in wind speed exhibited power differences as much as 500-kW for given imbalance cases. Additionally, the results indicated that a 10% variation in pitch angle, and blade mass density demonstrated power differences of 20-kW and 10-kW respectively due to imbalance in one blade. In addition, probability distributions for power output and dynamic loading indicated that turbine underperformance and excessive blade loading occurred approximately 40–52% and 45–77% of the time respectively depending on the imbalance scenario. This imbalance detection strategy could serve as a useful tool to help minimize turbine operation uncertainties.

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Yin, Shih-Hsun, and Bogdan I. Epureanu. "High-Sensitivity Mass Sensing Based on Enhanced Nonlinear Dynamics and Attractor Morphing Modes." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15648.

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This paper demonstrates two novel methods for identifying small parametric variations in an experimental system based on the analysis of sensitivity vector fields (SVFs) and probability density functions (PDFs). The experimental system includes a smart sensing beam excited by a nonlinear feedback excitation through two PZT (lead zirconate titanate) patches symmetrically bonded on both sides at the root of the beam. The nonlinear feedback excitation requires the measurement of the dynamics (e.g. velocity of one point at the tip of the beam) and a nonlinear feedback loop, and is designed such that the beam vibrates in a chaotic regime. Changes in the state space attractor of the dynamics due to small parametric variations can be captured by SVFs which, in turn, are collected by applying point cloud averaging (PCA) to points distributed in the attractors for nominal and changed parameters. Also, the PDFs characterize statistically the distribution of points in the attractors. The differences between the PDFs of the attractors for different changed parameters and the baseline attractor can provide different attractor morphing modes for identifying variations in distinct parameters. The experimental results based on the proposed approaches show that very small amounts of added mass at different locations along the beam can be accurately identified.

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Nieckele, Angela O., Mônica F. Naccache, Marcos S. P. Gomes, João E. Carneiro, and Ricardo Serfaty. "Models Evaluations of Combustion Process in a Cylindrical Furnace." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/htd-24232.

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Abstract In this work an evaluation of different combustion models for predicting oxygen enriched combustion processes was performed. Two types of models were selected. The first one was a generalized finite rate model, in which the conservation equation for the mass concentration was solved, for all species present in the process. In this modeling approach, three different reaction rate expressions were considered. The second case was based on the PDF formulation, which consisted in solving the conservation equations for the mass fraction and its variance. In this second approach the species distributions were determined by assuming two different shapes for the probability density functions. The mass, momentum, energy and species or mass fraction conservation equations were numerically solved by a finite volume formulation. The two-equation κ-ε turbulence model was selected for solving the turbulent problem. Radiation was taken into account by the discrete transfer radiation model. After solution, the temperature and species concentration fields were compared with available experimental data. Although the PDF formulation involved the solution of a smaller number of equations, therefore consuming less computer time, the performance of the generalized finite rate model was superior in the present test cases.

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Звіти організацій з теми "Probability mass functions"

Daudelin, Francois, Lina Taing, Lucy Chen, Claudia Abreu Lopes, Adeniyi Francis Fagbamigbe, and Hamid Mehmood. Mapping WASH-related disease risk: A review of risk concepts and methods. United Nations University Institute for Water, Environment and Health, December 2021. http://dx.doi.org/10.53328/uxuo4751.

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The report provides a review of how risk is conceived of, modelled, and mapped in studies of infectious water, sanitation, and hygiene (WASH) related diseases. It focuses on spatial epidemiology of cholera, malaria and dengue to offer recommendations for the field of WASH-related disease risk mapping. The report notes a lack of consensus on the definition of disease risk in the literature, which limits the interpretability of the resulting analyses and could affect the quality of the design and direction of public health interventions. In addition, existing risk frameworks that consider disease incidence separately from community vulnerability have conceptual overlap in their components and conflate the probability and severity of disease risk into a single component. The report identifies four methods used to develop risk maps, i) observational, ii) index-based, iii) associative modelling and iv) mechanistic modelling. Observational methods are limited by a lack of historical data sets and their assumption that historical outcomes are representative of current and future risks. The more general index-based methods offer a highly flexible approach based on observed and modelled risks and can be used for partially qualitative or difficult-to-measure indicators, such as socioeconomic vulnerability. For multidimensional risk measures, indices representing different dimensions can be aggregated to form a composite index or be considered jointly without aggregation. The latter approach can distinguish between different types of disease risk such as outbreaks of high frequency/low intensity and low frequency/high intensity. Associative models, including machine learning and artificial intelligence (AI), are commonly used to measure current risk, future risk (short-term for early warning systems) or risk in areas with low data availability, but concerns about bias, privacy, trust, and accountability in algorithms can limit their application. In addition, they typically do not account for gender and demographic variables that allow risk analyses for different vulnerable groups. As an alternative, mechanistic models can be used for similar purposes as well as to create spatial measures of disease transmission efficiency or to model risk outcomes from hypothetical scenarios. Mechanistic models, however, are limited by their inability to capture locally specific transmission dynamics. The report recommends that future WASH-related disease risk mapping research: - Conceptualise risk as a function of the probability and severity of a disease risk event. Probability and severity can be disaggregated into sub-components. For outbreak-prone diseases, probability can be represented by a likelihood component while severity can be disaggregated into transmission and sensitivity sub-components, where sensitivity represents factors affecting health and socioeconomic outcomes of infection. -Employ jointly considered unaggregated indices to map multidimensional risk. Individual indices representing multiple dimensions of risk should be developed using a range of methods to take advantage of their relative strengths. -Develop and apply collaborative approaches with public health officials, development organizations and relevant stakeholders to identify appropriate interventions and priority levels for different types of risk, while ensuring the needs and values of users are met in an ethical and socially responsible manner. -Enhance identification of vulnerable populations by further disaggregating risk estimates and accounting for demographic and behavioural variables and using novel data sources such as big data and citizen science. This review is the first to focus solely on WASH-related disease risk mapping and modelling. The recommendations can be used as a guide for developing spatial epidemiology models in tandem with public health officials and to help detect and develop tailored responses to WASH-related disease outbreaks that meet the needs of vulnerable populations. The report’s main target audience is modellers, public health authorities and partners responsible for co-designing and implementing multi-sectoral health interventions, with a particular emphasis on facilitating the integration of health and WASH services delivery contributing to Sustainable Development Goals (SDG) 3 (good health and well-being) and 6 (clean water and sanitation).

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