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Journal articles on the topic 'Statistical examples'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Hare, Lynne B. "Statistical Engineering: Principles and Examples." Quality Engineering 24, no. 2 (April 2012): 153–61. http://dx.doi.org/10.1080/08982112.2012.641144.

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2

Seung, H. S., H. Sompolinsky, and N. Tishby. "Statistical mechanics of learning from examples." Physical Review A 45, no. 8 (April 1, 1992): 6056–91. http://dx.doi.org/10.1103/physreva.45.6056.

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3

Schonlau, Matthias, and Rosie Yuyan Zou. "The random forest algorithm for statistical learning." Stata Journal: Promoting communications on statistics and Stata 20, no. 1 (March 2020): 3–29. http://dx.doi.org/10.1177/1536867x20909688.

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Random forests (Breiman, 2001, Machine Learning 45: 5–32) is a statistical- or machine-learning algorithm for prediction. In this article, we introduce a corresponding new command, rforest. We overview the random forest algorithm and illustrate its use with two examples: The first example is a classification problem that predicts whether a credit card holder will default on his or her debt. The second example is a regression problem that predicts the logscaled number of shares of online news articles. We conclude with a discussion that summarizes key points demonstrated in the examples.
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4

Hwa, Rebecca. "Sample Selection for Statistical Parsing." Computational Linguistics 30, no. 3 (September 2004): 253–76. http://dx.doi.org/10.1162/0891201041850894.

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Corpus-based statistical parsing relies on using large quantities of annotated text as training examples. Building this kind of resource is expensive and labor-intensive. This work proposes to use sample selection to find helpful training examples and reduce human effort spent on annotating less informative ones. We consider several criteria for predicting whether unlabeled data might be a helpful training example. Experiments are performed across two syntactic learning tasks and within the single task of parsing across two learning models to compare the effect of different predictive criteria. We find that sample selection can significantly reduce the size of annotated training corpora and that uncertainty is a robust predictive criterion that can be easily applied to different learning models.
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5

Stanley, H. Eugene. "Correlated randomness: Some examples of exotic statistical physics." Pramana 64, no. 5 (May 2005): 645–60. http://dx.doi.org/10.1007/bf02704574.

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6

NAKAO, Kento, Yuta NARUKAWA, and Seiji MIYOSHI. "Statistical Mechanics of On-Line Learning Using Correlated Examples." IEICE Transactions on Information and Systems E94-D, no. 10 (2011): 1941–44. http://dx.doi.org/10.1587/transinf.e94.d.1941.

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7

Ziegel, Eric R., and Glenn A. Walker. "Common Statistical Methods for Clinical Research with SAS Examples." Technometrics 41, no. 2 (May 1999): 179. http://dx.doi.org/10.2307/1270753.

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8

Mooney, Christopher Z. "Bootstrap Statistical Inference: Examples and Evaluations for Political Science." American Journal of Political Science 40, no. 2 (May 1996): 570. http://dx.doi.org/10.2307/2111639.

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9

Scinto, Philip R. "Statistical Engineering Examples in the Engine Oil Additive Industry." Quality Engineering 23, no. 2 (March 2, 2011): 125–33. http://dx.doi.org/10.1080/08982112.2011.555439.

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10

Mvududu, Nyaradzo, and Gibbs Y. Kanyongo. "Using Real Life Examples to Teach Abstract Statistical Concepts." Teaching Statistics 33, no. 1 (January 9, 2011): 12–16. http://dx.doi.org/10.1111/j.1467-9639.2009.00404.x.

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11

Cecconi, Lorenzo, Laura Grisotto, Dolores Catelan, Corrado Lagazio, Veronica Berrocal, and Annibale Biggeri. "Preferential sampling and Bayesian geostatistics: Statistical modeling and examples." Statistical Methods in Medical Research 25, no. 4 (August 2016): 1224–43. http://dx.doi.org/10.1177/0962280216660409.

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12

HARLOW, D. GARY. "PROBABILITY VERSUS STATISTICAL MODELING: EXAMPLES FROM FATIGUE LIFE PREDICTION." International Journal of Reliability, Quality and Safety Engineering 12, no. 06 (December 2005): 535–50. http://dx.doi.org/10.1142/s0218539305002002.

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Probability analyses are increasingly being used for reliability and durability assessments for life prediction of engineered components and systems. Nevertheless, many of the current analyses are predominately statistical rather than probabilistic. Fatigue life prediction has historically been based on the safe-life or the crack growth approaches, both of which are empirically based. Consequently, they do not adequately reflect long-term operating conditions, or identify the sources and extent of their contributions to variability. A comparison between probability and statistical approaches for fatigue life prediction is developed herein. Using simple crack growth models, the variability inherent in S-N response can be related to key random variables that are readily identified in the models. The identification and quantification of these variables are paramount for predicting fatigue lives. The effectiveness of probability modeling compared to statistical methodologies is shown through the analysis of an extensive set of S-N data for 2024-T4 aluminum alloy. Subsequently, the probability approach is demonstrated with S-N data for SUJ2 steel, in which two distinct failure modes are operative. Variability associated with manufacturing and material variables are considered. The adoption of this technique to put life prediction on a sound scientific and probabilistic basis is recommended.
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13

JENČOVÁ, ANNA, and DÉNES PETZ. "SUFFICIENCY IN QUANTUM STATISTICAL INFERENCE: A SURVEY WITH EXAMPLES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 09, no. 03 (September 2006): 331–51. http://dx.doi.org/10.1142/s0219025706002408.

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This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated in parallel to the measure theoretic case. It turns out that several classical examples and results have a noncommutative analogue. Some of the results are presented without proof (but with exact references) and the presentation is intended to be self-contained. The main examples discussed in the paper are related to the Weyl algebra and to the exponential family of states. The characterization of sufficiency in terms of quantum Fisher information is a new result.
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14

Gaver, D. P., and J. P. Lehoczky. "Statistical analysis of hierarchical stochastic models: Examples and approaches." Annals of Operations Research 8, no. 1 (December 1987): 217–27. http://dx.doi.org/10.1007/bf02187093.

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15

Booltink, Harry. "Statistical Experiment Design and Interpretation, an introduction with agricultural examples." Agricultural Systems 68, no. 1 (April 2001): 93–94. http://dx.doi.org/10.1016/s0308-521x(00)00057-3.

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16

Gustavsson, M., L. Gillner, and C. P. Larsen. "Statistical analysis of interferometric crosstalk: theory and optical network examples." Journal of Lightwave Technology 15, no. 11 (1997): 2006–19. http://dx.doi.org/10.1109/50.641518.

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17

Delaharpe, P., and V. F. R. Jones. "Graph Invariants Related to Statistical Mechanical Models: Examples and Problems." Journal of Combinatorial Theory, Series B 57, no. 2 (March 1993): 207–27. http://dx.doi.org/10.1006/jctb.1993.1017.

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18

Fisher, N. I., and C. McA Powell. "Statistical analysis of two-dimensional palaeocurrent data: Methods and examples." Australian Journal of Earth Sciences 36, no. 1 (March 1989): 91–107. http://dx.doi.org/10.1080/14400958908527953.

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19

Hague, Howard. "Handling statistical enquiries in the medical library — some practical examples." Aslib Proceedings 38, no. 5 (May 1986): 169–75. http://dx.doi.org/10.1108/eb051010.

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20

Ghosal, Sanjoy, and Avishek Ghosh. "When deviation happens between rough statistical convergence and rough weighted statistical convergence." Mathematica Slovaca 69, no. 4 (August 27, 2019): 871–90. http://dx.doi.org/10.1515/ms-2017-0275.

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Abstract In this paper we introduce rough weighted statistical limit set and weighted statistical cluster points set which are natural generalizations of rough statistical limit set and statistical cluster points set of double sequences respectively. Some new examples are constructed to ensure the deviation of basic results. Both the sets don’t follow the usual extension properties which will be discussed here.
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21

Manea, Daniela-Ioana, Emilia Țiţan, Radu R. Șerban, and Mihaela Mihai. "Statistical applications of optimization methods and mathematical programming." Proceedings of the International Conference on Applied Statistics 1, no. 1 (October 1, 2019): 312–28. http://dx.doi.org/10.2478/icas-2019-0028.

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Abstract Optimization techniques perform an important role in different domains of statistic. Examples of parameter estimation of different distributions, correlation analysis (parametric and nonparametric), regression analysis, optimal allocation of resources in partial research, exploration of response surfaces, design of experiments, efficiency tests, reliability theory, survival analysis are the most known methods of statistical analysis in which we find optimization techniques. The paper contains a synthetic presentation of the main statistical methods using classical optimization techniques, numerical optimization methods, linear and nonlinear programming, variational calculus techniques. Also, an example of applying the “simplex” algorithm in making a decision to invest an amount on the stock exchange, using a prediction model..
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22

Opozda, Barbara. "Completeness in affine and statistical geometry." Annals of Global Analysis and Geometry 59, no. 3 (February 10, 2021): 367–83. http://dx.doi.org/10.1007/s10455-021-09752-x.

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AbstractWe begin the study of completeness of affine connections, especially those on statistical manifolds or on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
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23

Gudder, Stan. "Examples of quantum integrals." Reports on Mathematical Physics 66, no. 1 (August 2010): 21–41. http://dx.doi.org/10.1016/s0034-4877(10)00021-2.

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24

Chang, Lay Nam, and Yigao Liang. "Topological anomalies: Explicit examples." Communications in Mathematical Physics 108, no. 1 (March 1987): 139–52. http://dx.doi.org/10.1007/bf01210706.

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25

Pistone, Giovanni. "Examples of the Application of Nonparametric Information Geometry to Statistical Physics." Entropy 15, no. 12 (September 25, 2013): 4042–65. http://dx.doi.org/10.3390/e15104042.

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26

Buyse, Marc, Geert Molenberghs, Xavier Paoletti, Koji Oba, Ariel Alonso, Wim Van der Elst, and Tomasz Burzykowski. "Statistical evaluation of surrogate endpoints with examples from cancer clinical trials." Biometrical Journal 58, no. 1 (February 12, 2015): 104–32. http://dx.doi.org/10.1002/bimj.201400049.

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27

Guthrie, Katherine A., Hilary S. Gammill, Mads Kamper-Jørgensen, Anne Tjønneland, Vijayakrishna K. Gadi, J. Lee Nelson, and Wendy Leisenring. "Statistical Methods for Unusual Count Data: Examples From Studies of Microchimerism." American Journal of Epidemiology 184, no. 10 (October 21, 2016): 779–86. http://dx.doi.org/10.1093/aje/kww093.

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28

Shigematsu, H. "Statistical-thermodynamic approach to a chaotic dynamical system: Exactly solvable examples." Journal of Statistical Physics 59, no. 1-2 (April 1990): 257–97. http://dx.doi.org/10.1007/bf01015570.

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29

Vere-Jones, D., and T. Ozaki. "Corrections to “Some examples of statistical estimation applied to earthquake data”." Annals of the Institute of Statistical Mathematics 39, no. 1 (December 1987): 243. http://dx.doi.org/10.1007/bf02491463.

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30

Mallik, Abhirup. "Statistical Rethinking: A Bayesian Course with Examples in R and Stan." Technometrics 63, no. 3 (July 3, 2021): 440–41. http://dx.doi.org/10.1080/00401706.2021.1945329.

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31

Luginbuhl, Molly, John B. Rundle, and Donald L. Turcotte. "Statistical physics models for aftershocks and induced seismicity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2136 (November 26, 2018): 20170397. http://dx.doi.org/10.1098/rsta.2017.0397.

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A standard approach to quantifying the seismic hazard is the relative intensity (RI) method. It is assumed that the rate of seismicity is constant in time and the rate of occurrence of small earthquakes is extrapolated to large earthquakes using Gutenberg–Richter scaling. We introduce nowcasting to extend RI forecasting to time-dependent seismicity, for example, during an aftershock sequence. Nowcasting uses ‘natural time’; in seismicity natural time is the event count of small earthquakes. The event count for small earthquakes is extrapolated to larger earthquakes using Gutenberg–Richter scaling. We first review the concepts of natural time and nowcasting and then illustrate seismic nowcasting with three examples. We first consider the aftershock sequence of the 2004 Parkfield earthquake on the San Andreas fault in California. Some earthquakes have higher rates of aftershock activity than other earthquakes of the same magnitude. Our approach allows the determination of the rate in real time during the aftershock sequence. We also consider two examples of induced earthquakes. Large injections of waste water from petroleum extraction have generated high rates of induced seismicity in Oklahoma. The extraction of natural gas from the Groningen gas field in The Netherlands has also generated very damaging earthquakes. In order to reduce the seismic activity, rates of injection and withdrawal have been reduced in these two cases. We show how nowcasting can be used to assess the success of these efforts. This article is part of the theme issue ‘Statistical physics of fracture and earthquakes’.
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32

Antal, Reena, Meenakshi Chawla, and Vijay Kumar. "SOME REMARKS ON ROUGH STATISTICAL \(\Lambda\)-CONVERGENCE OF ORDER \(\alpha\)." Ural Mathematical Journal 7, no. 1 (July 30, 2021): 16. http://dx.doi.org/10.15826/umj.2021.1.002.

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The main purpose of this work is to define Rough Statistical \(\Lambda\)-Convergence of order \(\alpha\) \((0<\alpha\leq1)\) in normed linear spaces. We have proved some basic properties and also provided some examples to show that this method of convergence is more generalized than the rough statistical convergence. Further, we have shown the results related to statistically \(\Lambda\)-bounded sets of order \(\alpha\) and sets of rough statistically \(\Lambda\)-convergent sequences of order \(\alpha\).
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33

Pundik, Amit. "Statistical Evidence and Individual Litigants: A Reconsideration of Wasserman's Argument from Autonomy." International Journal of Evidence & Proof 12, no. 4 (November 2008): 303–24. http://dx.doi.org/10.1350/ijep.2008.12.4.304.

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The use of statistical evidence in court has attracted long-running controversy. Some uses of statistical evidence seem intuitively wrong, both in real cases (for example, Sally Clark) and in hypothetical examples (for example, the Gatecrasher Paradox). Yet, explaining why has proven to be difficult. One promising approach is that of Wasserman, who claims that using statistical evidence demeans the litigant's individuality and autonomy. This article presents Wasserman's argument, explores its merits, and defends it from some objections. However, the article also identifies six significant weaknesses, which have to be overcome before Wassermann's account can successfully identify the circumstances in which statistical evidence should be used or restricted.
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34

Averina, Tatiana A., Elena V. Karachanskaya, and Konstantin A. Rybakov. "Statistical analysis of diffusion systems with invariants." Russian Journal of Numerical Analysis and Mathematical Modelling 33, no. 1 (February 23, 2018): 1–13. http://dx.doi.org/10.1515/rnam-2018-0001.

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Abstract The aim of the paper is the construction and numerical solution of stochastic differential equations whose trajectories are located on a given smooth manifold with probability 1. Second order cylindrical surfaces, i.e., elliptic, hyperbolic, and parabolic cylinders serve as examples of such manifolds for the tree-dimensional space (the phase space is two-dimensional). Classes of stochastic differential equations are constructed for these surfaces and linear equations with multiplicative noise are marked in these classes. The results of modelling were used to estimate the deviations of numerical solutions from the manifold. A comparative analysis of considered examples was carried out for accuracy of eight numerical solution methods for stochastic differential equations.
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35

Bodzioch, Małgorzata, and Joachim Domsta. "Two Examples of Quantum Dynamical Semigroups." Open Systems & Information Dynamics 18, no. 02 (June 2011): 143–55. http://dx.doi.org/10.1142/s1230161211000091.

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The Hamiltonians of the considered bi-partite systems are of the form [Formula: see text] Subindex S corresponds to the observed system and R to the reservoir (the enviroment of S). Two classes of systems are distinguished: the discrete-continuous (D-C) and the continuous-continuous (C-C) models. In both cases resevoir operators MR and HR are of continuous spectrum type. In D-C models the operators HS and QS possess discrete spectra. In C-C models, the operators HS and QS are of continuous spectrum type. In each case of our examples the semigroup property for the reduced dynamics of system S is obtained under particular circumstances, depending on the diagonal of the density matrix of the reference state for R. In D-C models, due to discrete spectrum of QS, the semigroup property of the reduced dynamics of the reservoir R is shown to be impossible, unless the coupling to S is trivial.
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36

Weaver, Kenneth A. "Elaborating Selected Statistical Concepts with Common Experience." Teaching of Psychology 19, no. 3 (October 1992): 178–79. http://dx.doi.org/10.1207/s15328023top1903_17.

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Most statistics teachers strive to make the course material meaningful. This article presents specific examples for elaborating the statistical concepts of variability, null hypothesis testing, and confidence interval with common experience.
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37

Hirica, Iulia-Elena, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae, and Vasile Preda. "Affine Differential Geometric Control Tools for Statistical Manifolds." Mathematics 9, no. 14 (July 14, 2021): 1654. http://dx.doi.org/10.3390/math9141654.

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The paper generalizes and extends the notions of dual connections and of statistical manifold, with and without torsion. Links with the deformation algebras and with the Riemannian Rinehart algebras are established. The semi-Riemannian manifolds admitting flat dual connections with torsion are characterized, thus solving a problem suggested in 2000 by S. Amari and H. Nagaoka. New examples of statistical manifolds are constructed, within and beyond the classical setting. The invariant statistical structures on Lie groups are characterized and the dimension of their set is determined. Examples for the new defined geometrical objects are found in the theory of Information Geometry.
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38

HEMMECKE, RAYMOND, JASON MORTON, ANNE SHIU, BERND STURMFELS, and OLIVER WIENAND. "Three Counter-Examples on Semi-Graphoids." Combinatorics, Probability and Computing 17, no. 2 (March 2008): 239–57. http://dx.doi.org/10.1017/s0963548307008838.

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Semi-graphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection arrangement of the symmetric group Sn. In this paper we resolve two problems on semi-graphoids posed in Studený's book (2005), and we answer a related question of Postnikov, Reiner and Williams on generalized permutohedra. We also study the semigroup and the toric ideal associated with semi-graphoids.
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39

Pivato, Marcus. "A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACY." Episteme 9, no. 2 (June 2012): 115–37. http://dx.doi.org/10.1017/epi.2012.4.

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AbstractWe briefly review Condorcet's and Young's epistemic interpretations of preference aggregation rules as maximum likelihood estimators. We then develop a general framework for interpreting epistemic social choice rules as maximum likelihood estimators, maximum a posteriori estimators, or expected utility maximizers. We illustrate this framework with several examples. Finally, we critique this program.
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40

Khalili Golmankhaneh, Alireza. "Statistical Mechanics Involving Fractal Temperature." Fractal and Fractional 3, no. 2 (April 17, 2019): 20. http://dx.doi.org/10.3390/fractalfract3020020.

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In this paper, the Schrödinger equation involving a fractal time derivative is solved and corresponding eigenvalues and eigenfunctions are given. A partition function for fractal eigenvalues is defined. For generalizing thermodynamics, fractal temperature is considered, and adapted equations are defined. As an application, we present fractal Dulong-Petit, Debye, and Einstein solid models and corresponding fractal heat capacity. Furthermore, the density of states for fractal spaces with fractional dimension is obtained. Graphs and examples are given to show details.
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41

Nazar, Rogelio. "A statistical approach to term extraction." International Journal of English Studies 11, no. 2 (December 1, 2011): 159. http://dx.doi.org/10.6018/ijes/2011/2/149691.

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This paper argues in favor of a statistical approach to terminology extraction, general to all languages but with language specific parameters. In contrast to many application-oriented terminology studies, which are focused on a particular language and domain, this paper adopts some general principles of the statistical properties of terms and a method to obtain the corresponding language specific parameters. This method is used for the automatic identification of terminology and is quantitatively evaluated in an empirical study of English medical terms. The proposal is theoretically and computationally simple and disregards resources such as linguistic or ontological knowledge. The algorithm learns to identify terms during a training phase where it is shown examples of both terminological and non-terminological units. With these examples, the algorithm creates a model of the terminology that accounts for the frequency of lexical, morphological and syntactic elements of the terms in relation to the non-terminological vocabulary. The model is then used for the later identification of new terminology in previously unseen text. The comparative evaluation shows that performance is significantly higher than other well-known systems.
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42

Amarasingham, Asohan, Stuart Geman, and Matthew T. Harrison. "Ambiguity and nonidentifiability in the statistical analysis of neural codes." Proceedings of the National Academy of Sciences 112, no. 20 (May 1, 2015): 6455–60. http://dx.doi.org/10.1073/pnas.1506400112.

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Many experimental studies of neural coding rely on a statistical interpretation of the theoretical notion of the rate at which a neuron fires spikes. For example, neuroscientists often ask, “Does a population of neurons exhibit more synchronous spiking than one would expect from the covariability of their instantaneous firing rates?” For another example, “How much of a neuron’s observed spiking variability is caused by the variability of its instantaneous firing rate, and how much is caused by spike timing variability?” However, a neuron’s theoretical firing rate is not necessarily well-defined. Consequently, neuroscientific questions involving the theoretical firing rate do not have a meaning in isolation but can only be interpreted in light of additional statistical modeling choices. Ignoring this ambiguity can lead to inconsistent reasoning or wayward conclusions. We illustrate these issues with examples drawn from the neural-coding literature.
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43

Carey, Alan L. "Examples of odd index theorems." Reports on Mathematical Physics 57, no. 1 (February 2006): 41–51. http://dx.doi.org/10.1016/s0034-4877(06)80007-8.

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44

Barbella, Peter. "Realistic Examples in Elementary Statistics." Mathematics Teacher 80, no. 9 (December 1987): 740–43. http://dx.doi.org/10.5951/mt.80.9.0740.

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Secondary school students often do not see the need for certain statistical measures that we ask them to learn. Some statistics may seem redundant or to have no purpose at all. To the students, it may appear they are learning these statistics just for the sake of doing the calculations. Presented here are two examples including data sets for which calculating various elementary statistics will reveal something new about the data. The objective of these examples is to show the student what various statistics may reveal, or not reveal, about a given data set. Furthermore, questions can be raised regarding how various methods of analyzing data can lead to different or even contradictory conclusions.
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45

Holloway, Jacinta, and Kerrie Mengersen. "Statistical Machine Learning Methods and Remote Sensing for Sustainable Development Goals: A Review." Remote Sensing 10, no. 9 (August 28, 2018): 1365. http://dx.doi.org/10.3390/rs10091365.

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Interest in statistical analysis of remote sensing data to produce measurements of environment, agriculture, and sustainable development is established and continues to increase, and this is leading to a growing interaction between the earth science and statistical domains. With this in mind, we reviewed the literature on statistical machine learning methods commonly applied to remote sensing data. We focus particularly on applications related to the United Nations World Bank Sustainable Development Goals, including agriculture (food security), forests (life on land), and water (water quality). We provide a review of useful statistical machine learning methods, how they work in a remote sensing context, and examples of their application to these types of data in the literature. Rather than prescribing particular methods for specific applications, we provide guidance, examples, and case studies from the literature for the remote sensing practitioner and applied statistician. In the supplementary material, we also describe the necessary steps pre and post analysis for remote sensing data; the pre-processing and evaluation steps.
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46

Stefanowicz, Bogdan. "The power of statistical information." Wiadomości Statystyczne. The Polish Statistician 62, no. 4 (April 28, 2017): 25–33. http://dx.doi.org/10.5604/01.3001.0014.0891.

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The article aims at highlighting the phenomenon of statistical information as a medium of unique power (energy), which allows people to take reasonable measures in all areas of social, economic, political, and cultural life etc. For the research purpose the infological interpretation of the concept information and statistical information was used. In order to prove the thesis that statistical information has certain power, some features of statistical information were indicated herein and several examples of its function related to the practical use of such information were presented.
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47

MARTIN, PAUL P., and DAVID S. MCANALLY. "ON COMMUTANTS, DUAL PAIRS AND NON-SEMISIMPLE ALGEBRAS FROM STATISTICAL MECHANICS." International Journal of Modern Physics A 07, supp01b (April 1992): 675–705. http://dx.doi.org/10.1142/s0217751x92003987.

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For M a finite dimensional complex vector space and A a certain type of (unital) subalgebra of End(M) (including some specific types of physical significance in the field of quantum spin chains) we give an algorithm for constructing the centraliser or commutant B of A on M. We give examples, and discuss the conditions for centralising to be an involution, i.e. A, B a dual pair, and for B and A to be Morita equivalent. A special case of one example shows that Hn(q), Uq(sl2) act as a dual pair on the tensored vector representation for all q.
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48

Pinheiro, Jose C., Sylvie Hue, Annie Bouvier, Marie-Anne Gruet, and Emmanuel Jolivet. "Statistical Tools for Nonlinear Regression: A Practical Guide with S-PLUS Examples." Journal of the American Statistical Association 92, no. 439 (September 1997): 1219. http://dx.doi.org/10.2307/2965596.

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49

Linert, W. "The isokinetic relationship. VII. Statistical analyses and examples for unimolecular reaction systems." Inorganica Chimica Acta 141, no. 2 (January 1988): 233–42. http://dx.doi.org/10.1016/s0020-1693(00)83915-8.

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Linert, W. "The isokinetic relationship. VII. Statistical analyses and examples for unimolecular reaction systems." Inorganica Chimica Acta 149, no. 1 (September 1988): 155. http://dx.doi.org/10.1016/s0020-1693(00)90583-8.

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