Relevant bibliographies by topics / Probability Distributions Theory

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Probability Distributions Theory'

Author: Grafiati
Published: 5 June 2025
Last updated: 24 June 2025

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Journal articles on the topic "Probability Distributions Theory"

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Tarasov, Vasily E. "Nonlocal Probability Theory: General Fractional Calculus Approach." Mathematics 10, no. 20 (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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Bondesson, Lennart. "Factorization theory for probability distributions." Scandinavian Actuarial Journal 1995, no. 1 (1995): 44–53. http://dx.doi.org/10.1080/03461238.1995.10413949.

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Bondesson, L. "Factorization theory for probability distributions." Insurance: Mathematics and Economics 17, no. 3 (1996): 232. http://dx.doi.org/10.1016/0167-6687(96)82353-5.

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Blower, G., Z. J. Jurek, and J. D. Mason. "Operator-Limit Distributions in Probability Theory." Journal of the Royal Statistical Society. Series A (Statistics in Society) 158, no. 2 (1995): 352. http://dx.doi.org/10.2307/2983311.

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PE, Zbigniew J. Jurek, and J. David Mason. "Operator-Limit Distributions in Probability Theory." Journal of the American Statistical Association 89, no. 427 (1994): 1150. http://dx.doi.org/10.2307/2290967.

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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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Sekhon, Jasjeet. "Probability tests require distributions." Qualitative & Multi-Method Research 3, no. 1 (2005): 29–30. https://doi.org/10.5281/zenodo.998198.

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I applaud Goertz’s attempt at interpreting hypotheses about necessary conditions as probabilistic. As I discuss elsewhere in detail (Sekhon 2004), given the weakness of social science theories and the poor quality of our measurements, only probabilistic tests should be seriously considered. However, the move from deterministic theory to probabilistic testing is not a simple one. Although many difficult issues arise, I will here only discuss one: the issue of what distributions are required to conduct probabilistic tests and where they come from. Deterministic theories, by their very nature, do not say anything about the probability distributions in play. But the precise distributions used in any empirical test have profound implications. An interesting recent case of the confusion which can arise if one is not careful about this issue when comparing competing formal models is discussed and clarified by Wand (2005). I am also dubious that deterministic theories in general can be fixed ex post by adding stochastic terms instead of incorporating them from the beginning. For example, one has to be careful when simply adding stochastic terms that the theory remains self-consistent.
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Adisa, Agbona Anthony, Odukoya Elijah Ayooluwa, Amalare Asimi, and Ayeni Taiwo Michael. "Exponential-Gamma-Rayleigh Distribution: Theory and Properties." Asian Journal of Probability and Statistics 27, no. 3 (2025): 134–44. https://doi.org/10.9734/ajpas/2025/v27i3730.

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The use of traditional probability models to forecast real-world events is causing growing dissatisfaction among scholars. One of the motives could be the tail characteristics and goodness of fit metrics has a constraining tendency. Subsequently, there has been a significant increase in the generalisation of well-known probability distributions in recent years. The challenge is finding families versatile enough to fit both skewed and symmetric data. It is essential to understand that most generalised distributions described in the literature were developed using the generalised transformed transformer (T-X) method. This method was proposed by Alzaatreh et al. (2013). Also, Adewusi et al. (2019) showed that this generalization approach is beneficial by transforming the Exponential-Gamma distribution developed by Ogunwale et al. (2019) to a family of distribution known as the Exponential-Gamma-X. Therefore, in this study, we focused on developing a new family of continuous distributions called the Exponential-Gamma-Rayleigh distribution by transforming the newly generated continuous T-X family of distribution called the Exponential-Gamma-X distribution using the traditionally existing Rayleigh distribution as a transformer “X”. Several expressions for the new distribution’s theory and properties were explored and obtained; the maximum likelihood estimation approach was used to estimate the distributions' parameters, and finally, simulations studies were conducted to assess the asymptotic behaviour of the estimates.
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Joseph, Lawrence, and Caroline Reinhold. "Introduction to Probability Theory and Sampling Distributions." American Journal of Roentgenology 180, no. 4 (2003): 917–23. http://dx.doi.org/10.2214/ajr.180.4.1800917.

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Fan, Zhaozhi. "Semi-stable distributions in free probability theory." Science in China Series A 49, no. 3 (2006): 387–97. http://dx.doi.org/10.1007/s11425-006-0387-z.

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Dissertations / Theses on the topic "Probability Distributions Theory"

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Giamouridis, Daniel. "Implied probability distributions : estimation, testing and applications." Thesis, City University London, 2001. http://openaccess.city.ac.uk/8388/.

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A relatively large number of authors have proposed alternative techniques for the estimation of implied risk-neutral densities. As a general rule, an assumption for a theoretical equilibrium option pricing model is made and with the use of cross-sections of observed options prices point estimates of the risk-neutral probability densities are obtained. The present study is primarily concerned with the estimation of implied riskneutral densities by means of a semi-parametric Edgeworth Series Expansion probability model as an alternative to the widely criticized log-normal parameterization of the Black, Scholes and Merton model. Despite the relatively early introduction of this type of models in academic literature in the early '80s, it was not until the mid '90s that people started showing interest in their applications. Moreover, no studies by means of the Edgeworth Series Expansion probability model have so far been conducted with American style options. To this end, the present work initially develops the general theoretical framework and the numerical algorithm for the estimation of implied risk-neutral densities of the Edgeworth Series Expansion type from options prices. The technique is applicable to European options written on a generalized asset that pays dividends in continuous time or American futures options. The empirical part of the study considers data for the Oil and the Interest rates markets. The first task in the empirical investigation is to address general concerns with regard to the validity of an implied risk-neutral density estimation technique and its ability to stimulate meaningful discussion. To this end, the consistency of the Edgeworth Series Expansion type implied densities with the data is checked. This consistency is viewed in a broader sense: internal consistency - adequate fit to observed data - and economic rationale of the respective densities. An analysis is, therefore, performed to examine the properties of the implied densities in the presence of large changes in economic conditions. More specifically, the ability of the implied Edgeworth Series Expansion type implied densities to capture speculation over future eventualities and their capacity to immediately reflect changes in the market sentiment are examined. Motivated by existing concerns in the literature that the differences between the estimates from an alternative parameterization and the log-normal Black-Scholes-Merton parameterization may be apparent - better fit to observed data - but not significant.
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Anabila, Moses A. "Skew Pareto distributions." abstract and full text PDF (free order & download UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1453191.

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Feng, Jingyu. "Modeling Distributions of Test Scores with Mixtures of Beta Distributions." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1068.pdf.

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Ma, Kin-Keung. "Infinite prefix codes for geometric distributions /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?COMP%202004%20MA.

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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004.<br>Includes bibliographical references (leaves 74-76). Also available in electronic version. Access restricted to campus users.
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Merrell, Paul Clark. "Structure from Motion Using Optical Flow Probability Distributions." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd764.pdf.

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Lai, Pik-ying, and 黎碧瑩. "Lp regression under general error distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30287844.

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Wahed, Abdus S. "General families of skew-symmetric distributions." Virtual Press, 2000. http://liblink.bsu.edu/uhtbin/catkey/1178355.

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The family of univariate skew-normal probability distributions, an extension of symmetric normal distribution to a general case of asymmetry, was originally proposed by Azzalani [1]. Since its introduction, very limited research has been conducted in this area. An extension of the univariate skew-normal distribution to the multivariate case was considered by Azzalani and Dalla Valle [4]. Its application in statistics was recently considered by Azzalani and Capitanio [3]. As a general result, Azzalani (1985) [See [1]] showed that, any symmetric distribution can be viewed as a member of a more general class of skewed distributions.In this study we establish some properties of general family of skewed distributions. Examples of general family of asymmetric distributions is presented in a way to show their differences from the corresponding symmetric distributions. The skew-logistic distribution and its properties are considered in great details.<br>Department of Mathematical Sciences
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Majumder, M. Mahbubul A. "On Tukey's gh family of distributions." Virtual Press, 2007. http://liblink.bsu.edu/uhtbin/catkey/1371472.

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Skewness and elongation are two factors that directly determine the shape of a probability distribution. Thus, to obtain a flexible distribution it is always desirable that the parameters of the distribution directly determine the skewness and elongation. To meet this purpose, Tukey (1977) introduced a family of distributions called g-and-h family (gh family) based on a transformation of the standard normal variable where g and h determine the skewness and the elongation, respectively. The gh family of distributions was extensively studied by Hoaglin (1985) and Martinez and Iglewicz (1984). For its flexibility in shape He and Raghunathan (2006) have used this distribution for multiple imputations. Because of the complex nature of this family of distributions, it is not possible to have an explicit mathematical form of the density function and the estimates of the parameters g and h fully depend on extensive numerical computations.In this study, we have developed algorithms to numerically compute the density functions. We present algorithms to obtain the estimates of g and h using method of moments, quantile method and maximum likelihood method. We analyze the performance of each method and compare them using simulation technique. Finally, we study some special cases of gh family and their properties.<br>Department of Mathematical Sciences
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Millar, R. B. "Estimation of mixing and mixed distributions /." Thesis, Connect to this title online; UW restricted, 1989. http://hdl.handle.net/1773/8984.

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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.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Master<br>Master of Philosophy
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Books on the topic "Probability Distributions Theory"

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Callaway, Edgar H. Probability distributions. Addison-Wesley, 1993.

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

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Jurek, Zbigniew J. Operator-limit distributions in probability theory. Wiley, 1993.

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

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

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K, Kocherlakota, ed. Bivariate discrete distributions. M. Dekker, 1992.

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T︠S︡it︠s︡iashvili, G. Sh. Distributions in stochastic network models. Nova Science Publishers, 2008.

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Wimmer, Gejza. Thesaurus of univariate discrete probability distributions. Stamm, 1999.

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Charalambides, Ch A. Discrete q-distributions. John Wiley & Sons, 2016.

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

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Book chapters on the topic "Probability Distributions Theory"

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Klenke, Achim. "Infinitely Divisible Distributions." In Probability Theory. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56402-5_16.

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Klenke, Achim. "Infinitely Divisible Distributions." In Probability Theory. Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-5361-0_16.

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Sinai, Yakov G. "Multivariate Normal Distributions." In Probability Theory. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02845-2_9.

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Borda, Monica, Romulus Terebes, Raul Malutan, et al. "Probability Distributions." In Randomness and Elements of Decision Theory Applied to Signals. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-90314-5_2.

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Hausner, Melvin. "Some Standard Distributions." In Elementary Probability Theory. Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-1753-5_7.

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Robinson, Enders A. "Univariate Distributions." In Probability Theory and Applications. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5386-4_3.

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Robinson, Enders A. "Multivariate Distributions." In Probability Theory and Applications. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5386-4_5.

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Borovkov, Alexandr A. "On Convergence of Random Variables and Distributions." In Probability Theory. Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-5201-9_6.

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Robinson, Enders A. "Basic Discrete Distributions." In Probability Theory and Applications. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5386-4_7.

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Robinson, Enders A. "Basic Continuous Distributions." In Probability Theory and Applications. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5386-4_8.

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Conference papers on the topic "Probability Distributions Theory"

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Wang, Yichuan, Peipei Li, Xin Song, Yeqiu Xiao, and Xiaoxue Liu. "Probability analysis of system vulnerability distribution based on the matroid theory." In 2024 International Conference on Networking and Network Applications (NaNA). IEEE, 2024. http://dx.doi.org/10.1109/nana63151.2024.00023.

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Ogunwale, Olukunle Daniel, Kehinde Peter Ajewole, Korede Peter Olayinka, Ezekiel Olaoluwa Omole, Femi Emmanuel Amoyedo, and Oluwadamilare J. Akinremi. "A New Family of Continuous Probability Distribution: Gamma-Exponential Distribution (GED)Theory and its Properties." In 2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG). IEEE, 2024. http://dx.doi.org/10.1109/seb4sdg60871.2024.10630048.

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Mukherjee, Manuj, Aslan Tchamkerten, and Mansoor Yousefi. "Approximating Probability Distributions by ReLU Networks." In 2020 IEEE Information Theory Workshop (ITW). IEEE, 2021. http://dx.doi.org/10.1109/itw46852.2021.9457598.

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Lee, David, and Jehoshua Bruck. "Generating probability distributions using multivalued stochastic relay circuits." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6034134.

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Jacobs, Bart. "Partitions and Ewens Distributions in element-free Probability Theory." In LICS '22: 37th Annual ACM/IEEE Symposium on Logic in Computer Science. ACM, 2022. http://dx.doi.org/10.1145/3531130.3532419.

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Kogan, Eugene, and Moshe Kaveh. "Probability Distributions for Diffusive Light." In Advances in Optical Imaging and Photon Migration. Optica Publishing Group, 1996. http://dx.doi.org/10.1364/aoipm.1996.trit80.

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Statistical properties of coherent radiation propagating in a quasi-ID random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission coefficient are obtained.
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Choi, Chak Fung, and Cheuk Ting Li. "Multiple-Output Channel Simulation and Lossy Compression of Probability Distributions." In 2021 IEEE Information Theory Workshop (ITW). IEEE, 2021. http://dx.doi.org/10.1109/itw48936.2021.9611421.

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Huber, Michael. "Authentication and secrecy codes for equiprobable source probability distributions." In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5206028.

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Diakonikolas, Ilias, Themis Gouleakis, Daniel M. Kane, John Peebles, and Eric Price. "Optimal testing of discrete distributions with high probability." In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing. ACM, 2021. http://dx.doi.org/10.1145/3406325.3450997.

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Jiang, Yong, Shu-Tao Xia, Xin-Ji Liu, and Fang-Wei Fu. "Incorrigible set distributions and unsuccessful decoding probability of linear codes." In 2013 IEEE International Symposium on Information Theory (ISIT). IEEE, 2013. http://dx.doi.org/10.1109/isit.2013.6620385.

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Reports on the topic "Probability Distributions Theory"

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Aguilar, Alicia, and Ricardo Gimeno. Discrete Probability Forecasts: What to expect when you are expecting a monetary policy decision. Banco de España, 2024. http://dx.doi.org/10.53479/37893.

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We apply discrete probability forecasts to the expectations of monetary policy rate changes, both in the United States and in the euro area. By using binomial trees from options theory, forecast distributions are derived from the instantaneous forward yield curve, based on interest rate swaps. We then use a non-randomised discrete probability forecast evaluation that confirms the presence of a systematic upward bias, consistent with the presence of a term premium. Consequently, we propose a bias-correction methodology to increase the accuracy of the density forecasts regarding monetary policy expectations. This research provides pivotal insights into understanding and improving predictive tools in monetary policy forecasting.
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Pasupuleti, Murali Krishna. Phase Transitions in High-Dimensional Learning: Understanding the Scaling Limits of Efficient Algorithms. National Education Services, 2025. https://doi.org/10.62311/nesx/rr1125.

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Abstract: High-dimensional learning models exhibit phase transitions, where small changes in model complexity, data size, or optimization dynamics lead to abrupt shifts in generalization, efficiency, and computational feasibility. Understanding these transitions is crucial for scaling modern machine learning algorithms and identifying critical thresholds in optimization and generalization performance. This research explores the role of high-dimensional probability, random matrix theory, and statistical physics in analyzing phase transitions in neural networks, kernel methods, and convex vs. non-convex optimization. Key focus areas include the computational-to-statistical gap, double descent phenomena, and spectral phase transitions that impact model efficiency. The study also investigates the scaling limits of iterative optimization methods, highlighting when gradient-based learning succeeds or fails in high-dimensional regimes. By integrating theoretical analysis and empirical validation, this report provides a structured framework for designing scalable, efficient, and robust AI systems that can adapt to phase transitions and scaling laws in high-dimensional learning. Keywords: Phase transitions in learning, high-dimensional probability, scaling laws, statistical physics in AI, random matrix theory, computational-to-statistical gap, neural network overparameterization, double descent phenomenon, convex vs. non-convex optimization, spectral phase transitions, kernel methods in high dimensions, scaling limits in deep learning, gradient-based optimization, iterative learning algorithms, eigenvalue distributions in machine learning, large-scale AI efficiency, threshold effects in generalization, scaling-aware machine learning, AI robustness in high dimensions.
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Sullivan, Keith M., and Ian Grivell. QSIM: A Queueing Theory Model with Various Probability Distribution Functions. Defense Technical Information Center, 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, 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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Mariscal, Rodrigo, and Andrew Powell. Forecasting Inflation Risks in Latin America: A Technical Note. Inter-American Development Bank, 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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7

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), 2012. http://dx.doi.org/10.2172/1045758.

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8

Castro, Lucio, and Carlos Scartascini. Research Insights: How Do Messages Affect Taxpayers’ Behavior? Inter-American Development Bank, 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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Clark, Todd E., Gergely Ganics, and Elmar Mertens. What is the predictive value of SPF point and density forecasts? Federal Reserve Bank of Cleveland, 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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10

Bukstein, Daniel, and Néstor Gandelman. Glass Ceiling in Research: Evidence from a National Program in Uruguay. Inter-American Development Bank, 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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