Journal articles: 'Geometric statistics'

1

Berry, M. V., and Pragya Shukla. "Geometric Phase Curvature Statistics." Journal of Statistical Physics 180, no. 1-6 (October 9, 2019): 297–303. http://dx.doi.org/10.1007/s10955-019-02400-6.

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Constantin, Peter. "Geometric Statistics in Turbulence." SIAM Review 36, no. 1 (March 1994): 73–98. http://dx.doi.org/10.1137/1036004.

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3

Drew, Donald A. "Evolution of Geometric Statistics." SIAM Journal on Applied Mathematics 50, no. 3 (June 1990): 649–66. http://dx.doi.org/10.1137/0150038.

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4

Grady, D. E., and M. E. Kipp. "Geometric statistics and dynamic fragmentation." Journal of Applied Physics 58, no. 3 (August 1985): 1210–22. http://dx.doi.org/10.1063/1.336139.

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5

Timonin, P. N. "Statistics of geometric clusters in Potts model: statistical mechanics approach." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2240 (August 2020): 20200215. http://dx.doi.org/10.1098/rspa.2020.0215.

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The percolation of Potts spins with equal values in Potts model on graphs (networks) is considered. The general method for finding the Potts clusters' size distributions is developed. It allows full description of percolation transition when a giant cluster of equal-valued Potts spins appears. The method is applied to the short-ranged q-state ferromagnetic Potts model on the Bethe lattices with the arbitrary coordination number z . The analytical results for the field-temperature percolation phase diagram of geometric spin clusters and their size distribution are obtained. The last appears to be proportional to that of the classical non-correlated bond percolation with the bond probability, which depends on temperature and Potts model parameters.

6

Trofimov, V. K. "Encoding geometric sources with unknown statistics." Herald of the Siberian State University of Telecommunications and Informatics, no. 2 (June 18, 2021): 79–87. http://dx.doi.org/10.55648/1998-6920-2021-15-2-79-87.

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Universal encoding method of an arbitrary set of sources without memory generating letters of an infinite alphabet is proposed. The probabilities of the input alphabet letter appearance are a geometric progression. The proposed method is weakly universal for the set of all geometric sources. If the denominator of the geometric progression exceeds δ, δ > 0, the proposed encoding is universal. Redundancy estimates are obtained for an arbitrary subset of geometric sources.

7

Anevski, Dragi, Christopher Genovese, Geurt Jongbloed, and Wolfgang Polonik. "Statistics for Shape and Geometric Features." Oberwolfach Reports 13, no. 3 (2016): 1821–74. http://dx.doi.org/10.4171/owr/2016/32.

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Feragen, Aasa, Thomas Hotz, Stephan Huckemann, and Ezra Miller. "Statistics for Data with Geometric Structure." Oberwolfach Reports 15, no. 1 (January 4, 2019): 125–86. http://dx.doi.org/10.4171/owr/2018/3.

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9

ANASTOPOULOS, CHARIS. "SPIN-STATISTICS THEOREM AND GEOMETRIC QUANTIZATION." International Journal of Modern Physics A 19, no. 05 (February 20, 2004): 655–76. http://dx.doi.org/10.1142/s0217751x04017860.

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We study the relation of the spin-statistics theorem to the geometric structures on phase space, which are introduced in quantization procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the nonrelativistic domain (in fact for any symmetry group including internal symmetries) by requiring that the exchange can be implemented smoothly by a class of symmetry transformations that project in the phase space of the joint system system. We discuss the interpretation of this requirement, stressing the fact that any distinction of identical particles comes solely from the choice of coordinates — the exchange then arises from suitable change of coordinate system. We then examine our construction in the geometric and the coherent-state-path-integral quantization schemes. In the appendix we apply our results to exotic systems exhibiting continuous "spin" and "fractional statistics." This gives novel and unusual forms of the spin-statistics relation.

10

Dettmann, C. P., O. Georgiou, and G. Knight. "Spectral statistics of random geometric graphs." EPL (Europhysics Letters) 118, no. 1 (April 1, 2017): 18003. http://dx.doi.org/10.1209/0295-5075/118/18003.

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11

Fan, Jianqing, Hui-Nien Hung, and Wing-Hung Wong. "Geometric Understanding of Likelihood Ratio Statistics." Journal of the American Statistical Association 95, no. 451 (September 2000): 836–41. http://dx.doi.org/10.1080/01621459.2000.10474275.

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12

Chakraborty, Subrata, and Rameshwar D. Gupta. "Exponentiated Geometric Distribution: Another Generalization of Geometric Distribution." Communications in Statistics - Theory and Methods 44, no. 6 (May 17, 2013): 1143–57. http://dx.doi.org/10.1080/03610926.2012.763090.

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Matsen, Frederick A. "A Geometric Approach to Tree Shape Statistics." Systematic Biology 55, no. 4 (August 1, 2006): 652–61. http://dx.doi.org/10.1080/10635150600889617.

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14

Plotkin, B. I. "Geometric equivalence, geometric similarity, and geometric compatibility of algebras." Journal of Mathematical Sciences 140, no. 5 (February 2007): 716–28. http://dx.doi.org/10.1007/s10958-007-0011-y.

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15

Yang, Aijun, Hui Yu, and Zhenhai Yang. "The MLE of Geometric Parameter for a Geometric Process." Communications in Statistics - Theory and Methods 35, no. 10 (October 2006): 1921–30. http://dx.doi.org/10.1080/03610920600728609.

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16

Neill, James W., David J. Saville, and Graham R. Wood. "Statistical Methods: A Geometric Primer." Journal of the American Statistical Association 92, no. 440 (December 1997): 1652. http://dx.doi.org/10.2307/2965450.

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17

Davy, P. J., and J. C. W. Rayner. "Multivariate geometric distributions." Communications in Statistics - Theory and Methods 25, no. 12 (January 1996): 2971–87. http://dx.doi.org/10.1080/03610929608831881.

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18

Neill, James W., David J. Saville, and Graham R. Wood. "Statistical Methods: The Geometric Approach." American Statistician 47, no. 3 (August 1993): 234. http://dx.doi.org/10.2307/2684984.

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19

Rising, William. "Geometric Markov chains." Journal of Applied Probability 32, no. 2 (June 1995): 349–74. http://dx.doi.org/10.2307/3215293.

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A generalization of the familiar birth–death chain, called the geometric chain, is introduced and explored. By the introduction of two families of parameters in addition to the infinitesimal birth and death rates, the geometric chain allows transitions beyond the nearest neighbor, but is shown to retain the simple computational formulas of the birth–death chain for the stationary distribution and the expected first-passage times between states. It is also demonstrated that even when not reversible, a reversed geometric chain is again a geometric chain.

20

Hörfelt, Per. "Geometric bounds on certain sublinear functionals of geometric Brownian motion." Journal of Applied Probability 40, no. 4 (September 2003): 893–905. http://dx.doi.org/10.1239/jap/1067436089.

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Suppose that {Xs, 0 ≤ s ≤ T} is an m-dimensional geometric Brownian motion with drift, μ is a bounded positive Borel measure on [0,T], and ϕ : ℝm → [0,∞) is a (weighted) lq(ℝm)-norm, 1 ≤ q ≤ ∞. The purpose of this paper is to study the distribution and the moments of the random variable Y given by the Lp(μ)-norm, 1 ≤ p ≤ ∞, of the function s ↦ ϕ(Xs), 0 ≤ s ≤ T. By using various geometric inequalities in Wiener space, this paper gives upper and lower bounds for the distribution function of Y and proves that the distribution function is log-concave and absolutely continuous on every open subset of the distribution's support. Moreover, the paper derives tail probabilities, presents sharp moment inequalities, and shows that Y is indetermined by its moments. The paper will also discuss the so-called moment-matching method for the pricing of Asian-styled basket options.

21

Molchanov, Stanislav A. "Book Review: Geometric modeling in probability and statistics." Bulletin of the American Mathematical Society 55, no. 1 (May 26, 2017): 109–11. http://dx.doi.org/10.1090/bull/1582.

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22

Ohkubo, Jun, and Thomas Eggel. "Noncyclic and nonadiabatic geometric phase for counting statistics." Journal of Physics A: Mathematical and Theoretical 43, no. 42 (September 30, 2010): 425001. http://dx.doi.org/10.1088/1751-8113/43/42/425001.

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23

Herla, Florian, Gerard H. Roe, and Ben Marzeion. "Ensemble statistics of a geometric glacier length model." Annals of Glaciology 58, no. 75pt2 (July 2017): 130–35. http://dx.doi.org/10.1017/aog.2017.15.

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ABSTRACT A third-order linear glacier length model is used to analyze if the retreat of Hintereisferner in the Austrian Alps over the past 160 years is exceptional, or lies within the range of the natural variability inherent to a stationary climate. A detailed uncertainty analysis takes into account glacier geometry, model parameters and initial conditions. A Monte Carlo ensemble strengthens the result that the observed retreat cannot be explained by natural variability and therefore affirms regional climate change. Finally the observed temperature trend at Hintereisferner lies outside the range of natural variability from an ensemble of climate models, but is consistent with the modeled range of responses to anthropogenic forcing.

24

Ganapathi, Iyyakutti Iyappan, Syed Sadaf Ali, and Surya Prakash. "Geometric statistics-based descriptor for 3D ear recognition." Visual Computer 36, no. 1 (September 10, 2018): 161–73. http://dx.doi.org/10.1007/s00371-018-1593-8.

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25

Bandyopadhyay, P. "The geometric phase and the spin-statistics relation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2122 (May 5, 2010): 2917–32. http://dx.doi.org/10.1098/rspa.2010.0042.

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The exchange phase for two spins is studied here from the point of view of the quantization of a fermion in the framework of Nelson’s stochastic mechanics. This introduces a direction vector attached to a space–time point depicting the spin degrees of freedom. In this formalism, a fermion appears as a scalar particle attached with a magnetic-flux quantum, and a quantum spin can be described in terms of an SU(2) gauge bundle. This helps us to recast the Berry–Robbins formalism where the exchange phase appears as an unfamiliar geometric phase arising out of the ‘exchange rotation’ in a transported spin basis in terms of gauge currents. However, for polarized fermions, the exchange phase is found to be given by the Berry phase.

26

Zhao, Peng, and Feng Su. "On maximum order statistics from heterogeneous geometric variables." Annals of Operations Research 212, no. 1 (May 22, 2012): 215–23. http://dx.doi.org/10.1007/s10479-012-1158-6.

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27

Sathar, E. I. Abdul, and Veena L. Vijayan. "Quantile Based Geometric Vitality Function of Order Statistics." Mathematical Methods of Statistics 32, no. 1 (March 2023): 88–101. http://dx.doi.org/10.3103/s1066530723010040.

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28

Heikkilä, Matias. "Nonparametric geometric outlier detection." Scandinavian Journal of Statistics 46, no. 4 (June 4, 2019): 1300–1314. http://dx.doi.org/10.1111/sjos.12399.

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29

Chernyak, V. Y., M. Chertkov, and N. A. Sinitsyn. "The geometric universality of currents." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 09 (September 14, 2011): P09006. http://dx.doi.org/10.1088/1742-5468/2011/09/p09006.

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30

Tyurin, Yu N. "Multivariate Statistical Analysis: The Geometric Theory." Theory of Probability & Its Applications 55, no. 1 (January 2011): 91–109. http://dx.doi.org/10.1137/s0040585x97984620.

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31

Pulkin, I. S., and A. V. Tatarintsev. "Sufficient statistics for the Pareto distribution parameter." Russian Technological Journal 9, no. 3 (June 28, 2021): 88–97. http://dx.doi.org/10.32362/2500-316x-2021-9-3-88-97.

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The task of estimating the parameters of the Pareto distribution, first of all, of an indicator of this distribution for a given sample, is relevant. This article establishes that for this estimate, it is sufficient to know the product of the sample elements. It is proved that this product is a sufficient statistic for the Pareto distribution parameter. On the basis of the maximum likelihood method the distribution degree indicator is estimated. It is proved that this estimate is biased, and a formula eliminating the bias is justified. For the product of the sample elements considered as a random variable the distribution function and probability density are found; mathematical expectation, higher moments, and differential entropy are calculated. The corresponding graphs are built. In addition, it is noted that any function of this product is a sufficient statistic, in particular, the geometric mean. For the geometric mean also considered as a random variable, the distribution function, probability density, and the mathematical expectation are found; the higher moments, and the differential entropy are also calculated, and the corresponding graphs are plotted. In addition, it is proved that the geometric mean of the sample is a more convenient sufficient statistic from a practical point of view than the product of the sample elements. Also, on the basis of the Rao–Blackwell–Kolmogorov theorem, effective estimates of the Pareto distribution parameter are constructed. In conclusion, as an example, the technique developed here is applied to the exponential distribution. In this case, both the sum and the arithmetic mean of the sample can be used as sufficient statistics.

32

Mao, Tiantian, and Taizhong Hu. "EQUIVALENT CHARACTERIZATIONS ON ORDERINGS OF ORDER STATISTICS AND SAMPLE RANGES." Probability in the Engineering and Informational Sciences 24, no. 2 (March 18, 2010): 245–62. http://dx.doi.org/10.1017/s0269964809990258.

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The purpose of this article is to present several equivalent characterizations of comparing the largest-order statistics and sample ranges of two sets of n independent exponential random variables with respect to different stochastic orders, where the random variables in one set are heterogeneous and the random variables in the other set are identically distributed. The main results complement and extend several known results in the literature. The geometric distribution can be regarded as the discrete counterpart of the exponential distribution. We also study the orderings of the largest-order statistics from geometric random variables and point out similarities and differences between orderings of the largest-order statistics from geometric variables and from exponential variables.

33

Kozubowski, Tomasz J., Mark M. Meerschaert, Anna K. Panorska, and Hans-Peter Scheffler. "Operator geometric stable laws." Journal of Multivariate Analysis 92, no. 2 (February 2005): 298–323. http://dx.doi.org/10.1016/j.jmva.2003.09.004.

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34

Arciosa, Ramil M. "Cultural Statistics: Behind The Weaving Designs of T’nalak Tapestry." International Journal of Multidisciplinary: Applied Business and Education Research 5, no. 4 (April 24, 2024): 1423–33. http://dx.doi.org/10.11594/ijmaber.05.04.27.

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This research describes the multidisciplinary approach in between culture and mathematics/ science concepts, bounded with the different ethno modelling approaches. Like ethno modelling in math-ethno mathematics and physics-ethno physics The static value of the every IPs crafts man, evolve the statistical geometric patterns like the crystallize and geometric weaving designs, volume, areas and its skeletal designs most particularly in the geometric designs of some T’nalak handloom tapestry. When the artistic mind works, dynamism of neurons particles create a weaving designs and patterns with frequencies of wavelength that pointing in a symmetrical and elliptical rays of designs down to his affective and psychomotor of every T’nalak weavers, that’s include that application of cultural statistics. The cultural statistics based on the image processing analysis based on amplitude, wavelength and string theory in perfections of the unique designs of T’nalak weaving patterns.

35

Vakil, Ravi. "A geometric Littlewood–Richardson rule." Annals of Mathematics 164, no. 2 (September 1, 2006): 371–422. http://dx.doi.org/10.4007/annals.2006.164.371.

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36

McCartin, Brian J. "Geometric characterization of planar regression." Statistics 40, no. 3 (June 2006): 187–206. http://dx.doi.org/10.1080/02331880600665088.

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37

Cordeiro, Gauss M., Giovana O. Silva, and Edwin M. M. Ortega. "The beta-Weibull geometric distribution." Statistics 47, no. 4 (August 2013): 817–34. http://dx.doi.org/10.1080/02331888.2011.577897.

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38

Kundu, Debasis. "Multivariate geometric skew-normal distribution." Statistics 51, no. 6 (August 1, 2017): 1377–97. http://dx.doi.org/10.1080/02331888.2017.1355369.

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39

Dembińska, Anna. "kth records from geometric distribution." Statistics & Probability Letters 78, no. 12 (September 2008): 1662–70. http://dx.doi.org/10.1016/j.spl.2008.01.009.

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40

Nadarajah, Saralees, Vicente G. Cancho, and Edwin M. M. Ortega. "The geometric exponential Poisson distribution." Statistical Methods & Applications 22, no. 3 (May 9, 2013): 355–80. http://dx.doi.org/10.1007/s10260-013-0230-y.

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41

Kendall, Wilfrid. "Geometric Ergodicity and Perfect Simulation." Electronic Communications in Probability 9 (2004): 140–51. http://dx.doi.org/10.1214/ecp.v9-1117.

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42

Lunagómez, Simón, Sayan Mukherjee, Robert L. Wolpert, and Edoardo M. Airoldi. "Geometric Representations of Random Hypergraphs." Journal of the American Statistical Association 112, no. 517 (January 2, 2017): 363–83. http://dx.doi.org/10.1080/01621459.2016.1141686.

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43

Famoye, Felix, and Carl Lee. "Exponentiated-exponential geometric regression model." Journal of Applied Statistics 44, no. 16 (December 14, 2016): 2963–77. http://dx.doi.org/10.1080/02664763.2016.1267117.

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44

Mossel, Jorn, Guillaume Palacios, and Jean-Sébastien Caux. "Geometric quenches in quantum integrable systems." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 09 (September 23, 2010): L09001. http://dx.doi.org/10.1088/1742-5468/2010/09/l09001.

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45

Hackett, Timothy M., Sven G. Bilén, David J. Bell, and Martin W. Lo. "Geometric Approach for Analytical Approximations of Satellite Coverage Statistics." Journal of Spacecraft and Rockets 56, no. 5 (September 2019): 1286–99. http://dx.doi.org/10.2514/1.a34267.

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46

Dallas, A. C. "Characterizing the geometric distribution using expectations of order statistics." Journal of Applied Probability 24, no. 2 (June 1987): 534–39. http://dx.doi.org/10.2307/3214277.

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47

FANG, KaiTai, and YongDao ZHOU. "A note on statistics simulation for geometric probability problems." SCIENTIA SINICA Mathematica 41, no. 3 (April 1, 2011): 253–64. http://dx.doi.org/10.1360/012009-442.

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48

Dallas, A. C. "Characterizing the geometric distribution using expectations of order statistics." Journal of Applied Probability 24, no. 02 (June 1987): 534–39. http://dx.doi.org/10.1017/s002190020003117x.

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49

Khesin, B., J. Lenells, G. Misiołek, and S. C. Preston. "Geometry of Diffeomorphism Groups, Complete integrability and Geometric statistics." Geometric and Functional Analysis 23, no. 1 (February 2013): 334–66. http://dx.doi.org/10.1007/s00039-013-0210-2.

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50

Norris, Scott A., and Stephen J. Watson. "Geometric simulation and surface statistics of coarsening faceted surfaces." Acta Materialia 55, no. 19 (November 2007): 6444–52. http://dx.doi.org/10.1016/j.actamat.2007.08.014.

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Journal articles on the topic 'Geometric statistics'

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