Relevant bibliographies by topics / Distribution (probability theory)

Academic literature on the topic 'Distribution (probability theory)'

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Published: 4 June 2021
Last updated: 31 July 2024

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Journal articles on the topic "Distribution (probability theory)"

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Tarasov, Vasily E. "Nonlocal Probability Theory: General Fractional Calculus Approach." Mathematics 10, no. 20 (October 17, 2022): 3848. http://dx.doi.org/10.3390/math10203848.

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Nonlocal generalization of the standard (classical) probability theory of a continuous distribution on a positive semi-axis is proposed. An approach to the formulation of a nonlocal generalization of the standard probability theory based on the use of the general fractional calculus in the Luchko form is proposed. Some basic concepts of the nonlocal probability theory are proposed, including nonlocal (general fractional) generalizations of probability density, cumulative distribution functions, probability, average values, and characteristic functions. Nonlocality is described by the pairs of Sonin kernels that belong to the Luchko set. Properties of the general fractional probability density function and the general fractional cumulative distribution function are described. The truncated GF probability density function, truncated GF cumulative distribution function, and truncated GF average values are defined. Examples of the general fractional (GF) probability distributions, the corresponding probability density functions, and cumulative distribution functions are described. Nonlocal (general fractional) distributions are described, including generalizations of uniform, degenerate, and exponential type distributions; distributions with the Mittag-Leffler, power law, Prabhakar, Kilbas–Saigo functions; and distributions that are described as convolutions of the operator kernels and standard probability density.
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Fang, Zizhou, Kaixi Tan, and Ziyi Wang. "Fundamental results in probability theory." Highlights in Science, Engineering and Technology 49 (May 21, 2023): 464–69. http://dx.doi.org/10.54097/hset.v49i.8586.

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Probability theory is an area of mathematics that deals with the concept of likelihood. Probability theory is the mathematical foundation of statistical reasoning, and understanding how unpredictability impacts data is crucial for data scientists. Gaussian (normal) distribution is the most widely used distribution. It has two parameters which are mean and variance and easy to interpret. Also, the central limit theorem tells us that sums of independent random variables make the least number of assumptions. In addition, Poisson, Laplace, Beta, Pareto, Dirichelt, Binomial and Gamma Distributions are useful in different areas. The multivariate Gaussian is the most widely used joint probability density function. Covariance and correlation are used to measure the degree between two random variable’s X and Y. Chebyshev Inequality defines a topological space, which includes a sequence of elements, and let the sequence be called . Strong Law of Large Numbers Theorem use in large number of random variable in pairwise independent identically distributed and Renewal Theory is and example in Strong Law of Large Numbers Theorem.
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Zeina, Mohamed Bisher, Nizar Altounji, Mohammad Abobala, and Yasin Karmouta. "Introduction to Symbolic 2-Plithogenic Probability Theory." Galoitica: Journal of Mathematical Structures and Applications 7, no. 2 (2023): 18–30. http://dx.doi.org/10.54216/gjmsa.070202.

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In this paper we present for the first time the concept of symbolic plithogenic random variables and study its properties including expected value and variance. We build the plithogenic formal form of two important distributions that are exponential and uniform distributions. We find its probability density function and cumulative distribution function in its plithogenic form. We also derived its expected values and variance and the formulas of its random numbers generating. We finally present the fundamental form of plithogenic probability density and cumulative distribution functions. All the theorems were proved depending on algebraic approach using isomorphisms. This paper can be considered the base of symbolic plithogenic probability theory.
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Tarasov, Vasily E. "Fractional Probability Theory of Arbitrary Order." Fractal and Fractional 7, no. 2 (February 1, 2023): 137. http://dx.doi.org/10.3390/fractalfract7020137.

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A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability density function (fractional PDF) is proposed. The basic properties of the fractional PDF are proven. The definition of the fractional cumulative distribution function (fractional CDF) is also suggested, and the basic properties of these functions are also proven. It is proven that the proposed fractional cumulative distribution functions generate unique probability spaces that are interpreted as spaces of a fractional probability theory of arbitrary order. Various examples of the distributions of the fractional probability of arbitrary order, which are defined on finite intervals of the real line, are suggested.
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Taylor, G. C. "A Heuristic Review of some Ruin Theory Results." ASTIN Bulletin 15, no. 2 (November 1985): 73–88. http://dx.doi.org/10.2143/ast.15.2.2015020.

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AbstractThe paper deals with the renewal equation governing the infinite-time ruin probability. It is emphasized as intended to be no more than a pleasant ramble through a few scattered results. An interesting connection between ruin probability and a recursion formula for computation of the aggregate claims distribution is noted and discussed. The relation between danger of the claim size distribution and ruin probability is reexamined in the light of some recent results on stochastic dominance. Finally, suggestions are made as to the way in which the formula for ruin probability leads easily to conclusions about the effect on that probability of the long-tailedness of the claim size distribution. Stable distributions, in particular, are examined.
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ROY, S. M., and VIRENDRA SINGH. "CAUSAL QUANTUM MECHANICS TREATING POSITION AND MOMENTUM SYMMETRICALLY." Modern Physics Letters A 10, no. 08 (March 14, 1995): 709–16. http://dx.doi.org/10.1142/s0217732395000752.

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De Broglie and Bohm formulated a causal quantum mechanics with a phase space density whose integral over momentum reproduces the position probability density of the usual statistical quantum theory. We propose a causal quantum theory with a joint probability distribution such that the separate probability distributions for position and momentum agree with the usual quantum theory. Unlike the Wigner distribution the suggested distribution is positive-definite and obeys the Liouville condition.
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V. P. Singh, L. Zhang, and A. Rahimi. "Probability Distribution of Rainfall-Runoff Using Entropy Theory." Transactions of the ASABE 55, no. 5 (2012): 1733–44. http://dx.doi.org/10.13031/2013.42364.

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Kondratiev, Yuri G. "WHITE NOISE DISTRIBUTION THEORY (Probability and Stochastics Series)." Bulletin of the London Mathematical Society 32, no. 1 (January 2000): 119–20. http://dx.doi.org/10.1112/s0024609399306391.

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Bougoffa, Lazhar, and Panagiotis T. Krasopoulos. "Integral inequalities in probability theory revisited." Mathematical Gazette 105, no. 563 (June 21, 2021): 263–70. http://dx.doi.org/10.1017/mag.2021.56.

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Tillé, Yves. "Yet Another Attempt to Classify Positive Univariate Probability Distributions." Austrian Journal of Statistics 53, no. 3 (June 10, 2024): 87–101. http://dx.doi.org/10.17713/ajs.v53i3.1776.

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We propose an original classification of several discrete and continuous probability distributions. We establish links between these distributions, in particular the little known relationship between the negative hypergeometric distribution and the beta distribution. These relations allow us to propose a structure of relations which is summarized in graphic form.Our classification emphasises the analogy between certain discrete and continuous distributions. This analogy makes it possible to establish relations between the theory of point processes and the theory of survey sampling. It also makes it possible to envisage the use of link functions that are little used in generalised regression.
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Dissertations / Theses on the topic "Distribution (probability theory)"

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Elamir, Elsayed Ali Habib. "Probability distribution theory, generalisations and applications of L-moments." Thesis, Durham University, 2001. http://etheses.dur.ac.uk/3987/.

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In this thesis, we have studied L-moments and trimmed L-moments (TL-moments) which are both linear functions of order statistics. We have derived expressions for exact variances and covariances of sample L-moments and of sample TL-moments for any sample size n in terms of first and second-order moments of order statistics from small conceptual sample sizes, which do not depend on the actual sample size n. Moreover, we have established a theorem which characterises the normal distribution in terms of these second-order moments and the characterisation suggests a new test of normality. We have also derived a method of estimation based on TL-moments which gives zero weight to extreme observations. TL-moments have certain advantages over L-moments and method of moments. They exist whether or not the mean exists (for example the Cauchy distribution) and they are more robust to the presence of outliers. Also, we have investigated four methods for estimating the parameters of a symmetric lambda distribution: maximum likelihood method in the case of one parameter and L-moments, LQ-moments and TL-moments in the case of three parameters. The L-moments and TL-moments estimators are in closed form and simple to use, while numerical methods are required for the other two methods, maximum likelihood and LQ-moments. Because of the flexibility and the simplicity of the lambda distribution, it is useful in fitting data when, as is often the case, the underlying distribution is unknown. Also, we have studied the symmetric plotting position for quantile plot assuming a symmetric lambda distribution and conclude that the choice of the plotting position parameter depends upon the shape of the distribution. Finally, we propose exponentially weighted moving average (EWMA) control charts to monitor the process mean and dispersion using the sample L-mean and sample L-scale and charts based on trimmed versions of the same statistics. The proposed control charts limits are less influenced by extreme observations than classical EWMA control charts, and lead to tighter limits in the presence of out-of-control observations.
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Bright, Leslie William. "Matrix-analytic methods in applied probability /." Title page, table of contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phb855.pdf.

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Jónsson, Ragner H. "Adaptive subband coding of video using probability distribution models." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/14453.

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Słowiński, Witold. "Autonomous learning of domain models from probability distribution clusters." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=211059.

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Nontrivial domains can be difficult to understand and the task of encoding a model of such a domain can be difficult for a human expert, which is one of the fundamental problems of knowledge acquisition. Model learning provides a way to address this problem by allowing a predictive model of the domain's dynamics to be learnt algorithmically, without human supervision. Such models can provide insight about the domain to a human or aid in automated planning or reinforcement learning. This dissertation addresses the problem of how to learn a model of a continuous, dynamic domain, from sensory observations, through the discretisation of its continuous state space. The learning process is unsupervised in that there are no predefined goals, and it assumes no prior knowledge of the environment. Its outcome is a model consisting of a set of predictive cause-and-effect rules which describe changes in related variables over brief periods of time. We present a novel method for learning such a model, which is centred around the idea of discretising the state space by identifying clusters of uniform density in the probability density function of variables, which correspond to meaningful features of the state space. We show that using this method it is possible to learn models exhibiting predictive power. Secondly, we show that applying this discretisation process to two-dimensional vector variables in addition to scalar variables yields a better model than only applying it to scalar variables and we describe novel algorithms and data structures for discretising one- and two-dimensional spaces from observations. Finally, we demonstrate that this method can be useful for planning or decision making in some domains where the state space exhibits stable regions of high probability and transitional regions of lesser probability. We provide evidence for these claims by evaluating the model learning algorithm in two dynamic, continuous domains involving simulated physics: the OpenArena computer game and a two-dimensional simulation of a bouncing ball falling onto uneven terrain.
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Pashley, Peter J. "The analysis of latency data using the inverse Gaussian distribution /." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75343.

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The inverse Gaussian distribution is investigated as a basis for statistical analyses of skewed and possibly censored response times. This distribution arises from a random walk process, is a member of the exponential family, and admits the sample arithmetic and harmonic means as complete sufficient statistics. In addition, the inverse Gaussian provides a reasonable alternative to the more commonly used lognormal statistical model due to the attractive properties of its parameter estimates.
Three modifications were made to the basic distribution definition: adding a shift parameter to account for minimum latencies, allowing for Type I censoring, and convoluting two inverse Gaussian random variables in order to model components of response times. Corresponding parameter estimation and large sample test procedures were also developed.
Results from analysing two extensive sets of simple and two-choice reaction times suggest that shifting the origin and accounting for Type I censoring can substantially improve the reliability of inverse Gaussian parameter estimates. The results also indicate that the convolution model provides a convenient medium for probing underlying psychological processes.
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Cassady, Charles Richard. "The frequency distribution of availability." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-09052009-040624/.

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Ding, Xiqian, and 丁茜茜. "Some new statistical methods for a class of zero-truncated discrete distributions with applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2015. http://hdl.handle.net/10722/211126.

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Counting data without zero category often occur in various _elds. Examples include days of hospital stay for patients, numbers of publication for tenure-tracked faculty in a university, numbers of tra_c violation for drivers during a certain period and so on. A class of zero-truncated discrete models such as zero-truncated Poisson, zero-truncated binomial and zero-truncated negative-binomial distributions are proposed in literature to model such count data. In this thesis, firstly, literature review is presented in Chapter 1 on a class of commonly used univariate zero-truncated discrete distributions. In Chapter 2, a unified method is proposed to derive the distribution of the sum of i.i.d. zero-truncated distribution random variables, which has important applications in the construction of the shortest Clopper-Person confidence intervals of parameters of interest and in the calculation of the exact p-value of a two-sided test for small sample sizes in one sample problem. These problems are discussed in Section 2.4. Then a novel expectation-maximization (EM) algorithm is developed for calculating the maximum likelihood estimates (MLEs) of parameters in general zero-truncated discrete distributions. An important feature of the proposed EM algorithm is that the latent variables and the observed variables are independent, which is unusual in general EM-type algorithms. In addition, a unified minorization-maximization (MM) algorithm for obtaining the MLEs of parameters in a class of zero-truncated discrete distributions is provided. The first objective of Chapter 3 is to propose the multivariate zero-truncated Charlier series (ZTCS) distribution by developing its important distributional properties, and providing efficient MLE methods via a novel data augmentation in the framework of the EM algorithm. Since the joint marginal distribution of any r-dimensional sub-vector of the multivariate ZTCS random vector of dimension m is an r-dimensional zero-deated Charlier series (ZDCS) distribution (1 6 r < m), it is the second objective of Chapter 3 to propose a new family of multivariate zero-adjusted Charlier series (ZACS) distributions (including the multivariate ZDCS distribution as a special member) with a more flexible correlation structure by accounting for both inflation and deflation at zero. The corresponding distributional properties are explored and the associated MLE method via EM algorithm is provided for analyzing correlated count data.
published_or_final_version
Statistics and Actuarial Science
Master
Master of Philosophy
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Calhoun, Grayson Ford. "Limit theory for overfit models." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3359804.

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Thesis (Ph. D.)--University of California, San Diego, 2009.
Title from first page of PDF file (viewed July 23, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 104-109).
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Shahriari, Shahriar. "The Frechet distribution as an alternative model of extreme value data." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26735.

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The Frechet distribution was applied to a set of earthquake data in order to test its validity as a practical alternative distribution for extreme value data. It was concluded that the Frechet distribution was the best model representing that data set. Also, a Poisson model of occurrence could not be rejected for that data set. The combination of these two models resulted in a closed form unconditional extreme value distribution which was developed analytically. The appropriate statistical tests and sensitivity analyses were performed on the obtained model.
Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
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Mbah, Alfred Kubong. "On the theory of records and applications." [Tampa, Fla.] : University of South Florida, 2007. http://purl.fcla.edu/usf/dc/et/SFE0002216.

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Books on the topic "Distribution (probability theory)"

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Johnson, Norman Lloyd. Univariate discrete distributions. 2nd ed. New York: Wiley, 1992.

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Callaway, Edgar H. Probability distributions. Reading, Mass: Addison-Wesley, 1993.

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Johnson, Norman Lloyd. Univariate discrete distributions: Norman L. Johnson, Adrienne W. Kemp, Samuel Kotz. 3rd ed. Hoboken, NJ: Wiley, 2005.

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Prokhorov, Yu V. Probability Theory III: Stochastic Calculus. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998.

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Rothschild, V. Probabilitydistributions. New York: Wiley, 1986.

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Fang, Kʻai-Tʻai. Symmetric multivariate and related distributions. London: Chapman and Hall, 1990.

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Eberlein, Ernst. High Dimensional Probability. Basel: Birkhäuser Basel, 1998.

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Prokhorov, Yu V. Limit Theorems of Probability Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000.

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Hall, R. R. Divisors. Cambridge: Cambridge University Press, 2008.

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M, Cuadras C., Fortiana Josep, and Rodriguez-Lallena José A, eds. Distributions with given marginals and statistical modelling. Dordrecht: Kluwer Academic Publishers, 2002.

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Book chapters on the topic "Distribution (probability theory)"

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O’Hagan, Anthony. "Distribution theory." In Probability, 132–56. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-1211-3_6.

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Deshmukh, Shailaja R., and Akanksha S. Kashikar. "Distribution Function." In Probability Theory, 135–64. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781032619057-3.

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Borovkov, Alexandr A. "Random Variables and Distribution Functions." In Probability Theory, 31–63. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5201-9_3.

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Sinai, Yakov G. "Distribution Functions, Lebesgue Integrals and Mathematical Expectation." In Probability Theory, 95–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02845-2_11.

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Paris, J. B. "On the Distribution of Probability Functions in the Natural World." In Probability Theory, 125–45. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-015-9648-0_7.

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Galambos, Janos. "Transforms of Distribution." In Advanced Probability Theory, Second Edition,, 97–150. 2nd ed. Boca Raton: CRC Press, 2023. http://dx.doi.org/10.1201/9781003418191-3.

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Kátai, I. "Distribution of Q-Additive Function." In Probability Theory and Applications, 309–18. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2817-9_20.

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Fristedt, Bert, and Lawrence Gray. "Distribution Functions." In A Modern Approach to Probability Theory, 25–40. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4899-2837-5_3.

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Sunklodas, J. "Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal Distribution." In Limit Theorems of Probability Theory, 113–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04172-7_3.

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Proschan, Michael A., and Pamela A. Shaw. "More on Convergence in Distribution." In Essentials of Probability Theory for Statisticians, 183–99. Boca Raton : Taylor & Francis, 2016. | Series: Chapman & hall/CRC texts in statistical science series | “A CRC title.”: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315370576-9.

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Conference papers on the topic "Distribution (probability theory)"

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Shimada, Yoshihito. "White noise distribution theory and its application." In Noncommutative Harmonic Analysis with Applications to Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc78-0-21.

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Nakahara, Yuta, Shota Saito, Akira Kamatsuka, and Toshiyasu Matsushima. "Probability Distribution on Rooted Trees." In 2022 IEEE International Symposium on Information Theory (ISIT). IEEE, 2022. http://dx.doi.org/10.1109/isit50566.2022.9834481.

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Ioannou, Ioanna, Charalambos D. Charalambous, and Sergey Loyka. "Outage probability under channel distribution uncertainty." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6034119.

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Ejiri, Shinji. "Probability distribution functions in the finite density lattice QCD." In The 30th International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2012. http://dx.doi.org/10.22323/1.164.0089.

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Min, Youngjae, and Hye Won Chung. "Shallow Neural Network can Perfectly Classify an Object following Separable Probability Distribution." In 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019. http://dx.doi.org/10.1109/isit.2019.8849497.

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Yang, C. C. "Probability distribution of laser beam intensity after propagating through turbulent media." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.fk2.

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Laser beams experience random scattering when they are propagated in turbulent media. If the turbulences are strong and the propagation distance is long enough, the statistics of the laser beam intensity is expected to reach the saturation regime in which the intensity possesses a Gaussian probability distribution as a consequence of the central limit theorem. However, in many cases the condition for saturation is not reached, and K distributions, instead of Gaussian distributions, have been reported by experimentalists. To give interpretations for these distributions, although simple theoretical models were introduced, a more rigorous method is presented with more physical insight. The theory behind these K distributions includes the conceptions of double-scattering by large and small irregularities and narrow laser beamwidth. Statistical fourth moments of laser intensities are evaluated and discussed thoroughly to show different properties of K distribution from those of Gaussian distribution. In mathematical computations, the path integral technique is applied under the assumption of forward scattering.
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Camberos, Jose, and Jose Camberos. "Comparison of selected probability distribution functions for gasdynamic simulations inspired by kinetic theory." In 35th Aerospace Sciences Meeting and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1997. http://dx.doi.org/10.2514/6.1997-340.

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Cicalese, Ferdinando, Luisa Gargano, and Ugo Vaccaro. "How to find a joint probability distribution of minimum entropy (almost) given the marginals." In 2017 IEEE International Symposium on Information Theory (ISIT). IEEE, 2017. http://dx.doi.org/10.1109/isit.2017.8006914.

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Lure, Y. M., M. Gao, and C. C. Yang. "Probability distribution for the photocount associated with a K distribution for laser intensity." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.wx7.

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It is well known that the photocount possesses approximately a gamma probability density function when the detected optical intensity follows a negative-exponential distribution. In some problems of laser propagation through turbulent media, however, it has been shown that the detected laser intensity possesses a K distribution. Here the notation K represents a modified Bessel function with an imaginary argument. The probability density function for the photocount associated with such a K distribution for laser intensity is evaluated. The theory presented can be applied to two situations: (1) probability distribution for photon number in a certain time interval collected by a small detecting aperture; (2) probability distribution for photon number per unit time interval collected by a large detecting aperture. To this end, the probability distribution for the detected energy or detected power, depending on different situations, is computed first. For this purpose, a standard procedure in probability theory can be followed through using the characteristic function. Then a Poisson distribution is introduced to compute the probability distribution of the photocount. Different orders of K distribution are to be considered.
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Ejiri, Shinji. "Particle density probability distribution function and center symmetry breaking in finite density lattice gauge theories." In The 38th International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.396.0531.

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Reports on the topic "Distribution (probability theory)"

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Sullivan, Keith M., and Ian Grivell. QSIM: A Queueing Theory Model with Various Probability Distribution Functions. Fort Belvoir, VA: Defense Technical Information Center, March 2003. http://dx.doi.org/10.21236/ada414471.

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Méndez-Vizcaíno, Juan C., Alexander Guarín, César Anzola-Bravo, and Anderson Grajales-Olarte. Characterizing and Communicating the Balance of Risks of Macroeconomic Forecasts: A Predictive Density Approach for Colombia. Banco de la República, October 2021. http://dx.doi.org/10.32468/be.1178.

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Since July 2021, Banco de la República strengthened its forecasting process and communication instruments, by involving predictive densities on the projections of its models, PATACON and 4GM. This paper presents the main theoretical and empirical elements of the predictive density approach for macroeconomic forecasting. This model-based methodology allows to characterize the balance of risks of the economy, and quantify their effects through a joint probability distribution of forecasts. We estimate this distribution based on the simulation of DSGE models, preserving the general equilibrium relationships and their macroeconomic consistency. We also illustrate the technical criteria used to represent the prospective factors of risk through the probability distributions of shocks.
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Rheinberger, Christoph, and Nicolas Treich. Catastrophe aversion: social attitudes towards common fates. Fondation pour une culture de sécurité industrielle, June 2016. http://dx.doi.org/10.57071/882rpq.

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In light of climate change and other existential threats, policy commentators sometimes suggest that society should be more concerned about catastrophes. This document reflects on what is, or should be, society’s attitude toward such low-probability, high-impact events. The question underlying this analysis is how society considers (1) a major accident that leads to a large number of deaths; (2) a large number of small accidents that each kill one person, where the two situations lead to the same total number of deaths. We first explain how catastrophic risk can be conceived of as a spread in the distribution of losses, or a “more risky” distribution of risks. We then review studies from decision sciences, psychology, and behavioral economics that elicit people’s attitudes toward various social risks. This literature review finds more evidence against than in favor of catastrophe aversion. We address a number of possible behavioral explanations for these observations, then turn to social choice theory to examine how various social welfare functions handle catastrophic risk. We explain why catastrophe aversion may be in conflict with equity concerns and other-regarding preferences. Finally, we discuss current approaches to evaluate and regulate catastrophic risk, with a discussion of how it could be integrated into a benefit-cost analysis framework.
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4

Mariscal, Rodrigo, and Andrew Powell. Forecasting Inflation Risks in Latin America: A Technical Note. Inter-American Development Bank, June 2012. http://dx.doi.org/10.18235/0009040.

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There are many sources of inflation forecasts for Latin America. The International Monetary Fund, Latin Focus, the Economist Intelligence Unit and other consulting companies all offer inflation forecasts. However, these sources do not provide any probability measures regarding the risk of inflation. In some cases, Central Banks offer forecast and probability analyses but typically their models are not fully transparent. This technical note attempts to develop a relatively homogeneous set of methodologies and employs them to estimate inflation forecasts, probability distributions for those forecasts and hence probability measures of high inflation. The methodologies are based on both parametric and non-parametric estimation. Results are given for five countries in the region that have inflation targeting regimes.
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Kriegel, Francesco. Learning description logic axioms from discrete probability distributions over description graphs (Extended Version). Technische Universität Dresden, 2018. http://dx.doi.org/10.25368/2022.247.

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Description logics in their standard setting only allow for representing and reasoning with crisp knowledge without any degree of uncertainty. Of course, this is a serious shortcoming for use cases where it is impossible to perfectly determine the truth of a statement. For resolving this expressivity restriction, probabilistic variants of description logics have been introduced. Their model-theoretic semantics is built upon so-called probabilistic interpretations, that is, families of directed graphs the vertices and edges of which are labeled and for which there exists a probability measure on this graph family. Results of scientific experiments, e.g., in medicine, psychology, or biology, that are repeated several times can induce probabilistic interpretations in a natural way. In this document, we shall develop a suitable axiomatization technique for deducing terminological knowledge from the assertional data given in such probabilistic interpretations. More specifically, we consider a probabilistic variant of the description logic EL⊥, and provide a method for constructing a set of rules, so-called concept inclusions, from probabilistic interpretations in a sound and complete manner.
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Cai, H., M. Wang, A. Elgowainy, and J. Han. Updated greenhouse gas and criteria air pollutant emission factors and their probability distribution functions for electricity generating units. Office of Scientific and Technical Information (OSTI), July 2012. http://dx.doi.org/10.2172/1045758.

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Castro, Lucio, and Carlos Scartascini. Research Insights: How Do Messages Affect Taxpayers’ Behavior? Inter-American Development Bank, August 2023. http://dx.doi.org/10.18235/0005060.

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The results of a field experiment in Argentina indicate that taxpayers who received a deterrent message (describing the penalties for non-compliance) are more likely to comply with payment of taxes than taxpayers in the control group. After receiving reciprocity and peer effects messages, the probability of compliance increased for some contributors but decreased for others according to their underlying distribution of beliefs. The use of messages on tax bills influences taxpayers depending on their prior beliefs, the location of their residence, and whether or not they live in the city where they have to pay the tax.
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8

Clark, Todd E., Gergely Ganics, and Elmar Mertens. What is the predictive value of SPF point and density forecasts? Federal Reserve Bank of Cleveland, November 2022. http://dx.doi.org/10.26509/frbc-wp-202237.

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This paper presents a new approach to combining the information in point and density forecasts from the Survey of Professional Forecasters (SPF) and assesses the incremental value of the density forecasts. Our starting point is a model, developed in companion work, that constructs quarterly term structures of expectations and uncertainty from SPF point forecasts for quarterly fixed horizons and annual fixed events. We then employ entropic tilting to bring the density forecast information contained in the SPF’s probability bins to bear on the model estimates. In a novel application of entropic tilting, we let the resulting predictive densities exactly replicate the SPF’s probability bins. Our empirical analysis of SPF forecasts of GDP growth and inflation shows that tilting to the SPF’s probability bins can visibly affect our model-based predictive distributions. Yet in historical evaluations, tilting does not offer consistent benefits to forecast accuracy relative to the model-based densities that are centered on the SPF’s point forecasts and reflect the historical behavior of SPF forecast errors. That said, there can be periods in which tilting to the bin information helps forecast accuracy. Replication files are available at https://github.com/elmarmertens/ClarkGanicsMertensSPFfancharts
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Bukstein, Daniel, and Néstor Gandelman. Glass Ceiling in Research: Evidence from a National Program in Uruguay. Inter-American Development Bank, April 2017. http://dx.doi.org/10.18235/0011792.

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This paper presents evidence that female researchers have 7.1 percentage points lower probability of being accepted into the largest national research support program in Uruguay than male researchers. They also have lower research productivity than their male counterparts. Differences in observable characteristics explain 4.9 of the 7.1 percentage point gap. The gender gap is wider at the higher ranks of the program consistent with the existence of a glass ceiling. The results are robust to issues of bidirectionality (impact of research productivity on the probability of accessing the program and impact of the program on research productivity), joint determination and correlation of variables (e.g. having a Ph.D., publishing, and tutoring), and initial productivity effects (positive results at early stages may have long-term effects on career development). The paper presents three hypotheses for the gender gap (an original sin in the organization of the system, biases in the composition of evaluation committees, and differences in field of concentration) and finds some evidence for each. Glass ceilings are stronger in the fields where women are overrepresented among the applicants to the system: medical sciences, natural sciences, and humanities. Finally, it presents a counterfactual distribution of the program in the absence of discriminatory treatment of women and discusses the economic costs of the gender gap.
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Melgar, Natalia, and Máximo Rossi. A Cross-Country Analysis of the Risk Factors for Depression at the Micro and Macro Level. Inter-American Development Bank, September 2010. http://dx.doi.org/10.18235/0010995.

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Past research has provided evidence of the role of some personal characteristics as risk factors for depression. However, few studies have examined jointly their specific impact and whether country characteristics change the probability of being depressed. In general, this is due to the use of single-country databases. The aim of this paper is to extend previous findings by employing a much larger dataset and including the country effects mentioned above. The paper estimates probit models with country effects and explores linkages between specific environmental factors and depression using data from the 2007 Gallup Public Opinion Poll. Findings indicate that depression is positively related to being a woman, adulthood, divorce, widowhood, unemployment and low income. Moreover, there is evidence of the significant positive association between inequality and depression, especially for those living in urban areas. Finally, some populations characteristics facilitate depression (age distribution and religious affiliation).
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