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Journal articles on the topic 'Random variables'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Vos, Paul W. "Random Variables Aren’t Random." Mathematics 13, no. 5 (2025): 775. https://doi.org/10.3390/math13050775.

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This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We show how measure-theoretic probability provides a framework for modeling populations through distributions, leading to three key contributions. First, we establish that random variables, properly understood as measurable functions, can be fully characterized without appealing to infinite hypothetical samples. Second, we demonstrate how this perspective enabl

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2

Jovanovic Dolecek, Gordana. "Teaching Random Variables." U.Porto Journal of Engineering 7, no. 1 (2021): 10–15. http://dx.doi.org/10.24840/2183-6493_007.001_0003.

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This paper presents demo program for teaching random variables dedicated to demonstration and visualization of behaviour of the product of m independent uniform random variables. The demo is used as a complementary tool in the teaching Random signals and processes curriculum at the graduate level. The demo is made in MATLAB and utilizes all benefits provided by MATLAB, such as simplicity, and good graphic environment, interactive use, among others. Additionally, this demo is used with other demo programs, also made in MATLAB, in teaching/learning process of random variables. Students were very

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3

FLETCHER, M. E. "Introducing Random Variables." Teaching Mathematics and its Applications 5, no. 4 (1986): 191–92. http://dx.doi.org/10.1093/teamat/5.4.191.

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4

Assani, I. "distributed random variables." Duke Mathematical Journal 88, no. 2 (1997): 217–46. http://dx.doi.org/10.1215/s0012-7094-97-08808-6.

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5

Mendonça, Sandra, António Alberto Oliveira, Dinis Pestana, and Maria Luísa Rocha. "Count Random Variables." Encyclopedia 4, no. 3 (2024): 1367–80. http://dx.doi.org/10.3390/encyclopedia4030089.

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The observation of randomness patterns serves as guidance for the craft of probabilistic modelling. The most used count models—Binomial, Poisson, Negative Binomial—are the discrete Morris’ natural exponential families whose variance is at most quadratic on the mean, and the solutions of Katz–Panjer recurrence relation, aside from being members of the generalised power series and hypergeometric distribution families, and this accounts for their many advantageous characteristics. Some other basic count models are also described, as well as models with less obvious but useful randomness patterns

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6

Peköz, Erol, and Sheldon M. Ross. "COMPOUND RANDOM VARIABLES." Probability in the Engineering and Informational Sciences 18, no. 4 (2004): 473–84. http://dx.doi.org/10.1017/s0269964804184039.

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We give a probabilistic proof of an identity concerning the expectation of an arbitrary function of a compound random variable and then use this identity to obtain recursive formulas for the probability mass function of compound random variables when the compounding distribution is Poisson, binomial, negative binomial random, hypergeometric, logarithmic, or negative hypergeometric. We then show how to use simulation to efficiently estimate both the probability that a positive compound random variable is greater than a specified constant and the expected amount by which it exceeds that constant

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7

Nadarajah, Saralees, Emmanuel Afuecheta, and Stephen Chan. "Ordered random variables." OPSEARCH 56, no. 1 (2019): 344–66. http://dx.doi.org/10.1007/s12597-019-00355-6.

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8

Shapiro, Arnold F. "Fuzzy random variables." Insurance: Mathematics and Economics 44, no. 2 (2009): 307–14. http://dx.doi.org/10.1016/j.insmatheco.2008.05.008.

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9

Gil, M. "Fuzzy random variables." Information Sciences 133, no. 1-2 (2001): 1–2. http://dx.doi.org/10.1016/s0020-0255(01)00072-x.

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10

Hathaway, Richard J. "Clustering Random Variables." IETE Journal of Research 44, no. 4-5 (1998): 199–205. http://dx.doi.org/10.1080/03772063.1998.11416046.

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11

Good, P. "Exchangeable random variables." Bioinformatics 26, no. 17 (2010): 2214. http://dx.doi.org/10.1093/bioinformatics/btq297.

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12

Puri, Madan L., and Dan A. Ralescu. "Fuzzy random variables." Journal of Mathematical Analysis and Applications 114, no. 2 (1986): 409–22. http://dx.doi.org/10.1016/0022-247x(86)90093-4.

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13

Miranda, Enrique, Inés Couso, and Pedro Gil. "Random sets as imprecise random variables." Journal of Mathematical Analysis and Applications 307, no. 1 (2005): 32–47. http://dx.doi.org/10.1016/j.jmaa.2004.10.022.

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14

Il'inskii, Alexander, and Sofiya Ostrovska. "On Lin's Condition for Products of Random Variables." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 1 (2019): 79–85. http://dx.doi.org/10.15407/mag15.01.079.

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15

Hui, Stefen, and C. J. Park. "The Representation of Hypergeometric Random Variables using Independent Bernoulli Random Variables." Communications in Statistics - Theory and Methods 43, no. 19 (2013): 4103–8. http://dx.doi.org/10.1080/03610926.2012.705941.

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16

Sugiman, Ikuo. "A random CLT for dependent random variables." Journal of Multivariate Analysis 20, no. 2 (1986): 321–26. http://dx.doi.org/10.1016/0047-259x(86)90086-2.

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17

CHEN, JianBing, ZhiQiang WAN, and PengYan SONG. "Random function model for dependent random variables." SCIENTIA SINICA Physica, Mechanica & Astronomica 48, no. 1 (2017): 014609. http://dx.doi.org/10.1360/sspma2017-00107.

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18

Andrea, Montanari. "Estimating random variables from random sparse observations." European Transactions on Telecommunications 19, no. 4 (2008): 385–403. http://dx.doi.org/10.1002/ett.1289.

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19

Hershkorn, Stephen J., and Robin J. Chapman. "Symmetric Random Variables: 10461." American Mathematical Monthly 105, no. 7 (1998): 670. http://dx.doi.org/10.2307/2589265.

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20

Garreau, G. A., and G. P. Beaumont. "Probability and Random Variables." Mathematical Gazette 71, no. 456 (1987): 165. http://dx.doi.org/10.2307/3616526.

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21

Khurshid, Anwer, Zuhair A. Al-Hemari, and Shahid Kamal. "On Complex Random Variables." Pakistan Journal of Statistics and Operation Research 8, no. 3 (2012): 645. http://dx.doi.org/10.18187/pjsor.v8i3.534.

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22

Burke, Matthew M. "Random variables in Forth." ACM SIGFORTH Newsletter 3, no. 3 (1991): 21–24. http://dx.doi.org/10.1145/126517.126521.

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23

Vakhania, N. N., and G. Z. Chelidze. "Quaternion Gaussian Random Variables." Theory of Probability & Its Applications 54, no. 2 (2010): 363–69. http://dx.doi.org/10.1137/s0040585x97984176.

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24

Thompson, Peter. "Almost-Binomial Random Variables." College Mathematics Journal 33, no. 3 (2002): 235. http://dx.doi.org/10.2307/1559038.

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25

Kinney, John J., and James L. Kepner. "Generalised Geometric Random Variables." Teaching Statistics 17, no. 1 (1995): 7–9. http://dx.doi.org/10.1111/j.1467-9639.1995.tb00705.x.

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26

Müller, Norbert Th. "Computability on random variables." Theoretical Computer Science 219, no. 1-2 (1999): 287–99. http://dx.doi.org/10.1016/s0304-3975(98)00292-8.

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27

Feng, Yuhu. "Gaussian fuzzy random variables." Fuzzy Sets and Systems 111, no. 3 (2000): 325–30. http://dx.doi.org/10.1016/s0165-0114(98)00033-5.

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28

Devroye, Luc. "Simulating Bessel random variables." Statistics & Probability Letters 57, no. 3 (2002): 249–57. http://dx.doi.org/10.1016/s0167-7152(02)00055-x.

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29

Christoph, Gerd, and Karina Schreiber. "Discrete stable random variables." Statistics & Probability Letters 37, no. 3 (1998): 243–47. http://dx.doi.org/10.1016/s0167-7152(97)00123-5.

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30

Gao, Rong, Zhiqiang Zhang, Hamed Ahmadazde, and Dan A. Ralescu. "Complex uncertain random variables." Soft Computing 22, no. 17 (2017): 5817–24. http://dx.doi.org/10.1007/s00500-017-2717-1.

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31

Sparks, T., and G. P. Beaumont. "Probability and Random Variables." Statistician 36, no. 4 (1987): 419. http://dx.doi.org/10.2307/2348848.

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32

Spurrier, John D., and G. P. Beaumont. "Probability and Random Variables." Journal of the American Statistical Association 82, no. 399 (1987): 947. http://dx.doi.org/10.2307/2288812.

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33

Salt, D. W., and G. P. Beaumont. "Probability and Random Variables." Journal of the Royal Statistical Society. Series A (Statistics in Society) 151, no. 1 (1988): 222. http://dx.doi.org/10.2307/2982194.

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34

Fortet, R. "Probability and Random Variables." European Journal of Operational Research 29, no. 1 (1987): 115. http://dx.doi.org/10.1016/0377-2217(87)90203-7.

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35

Lenczewski, Romuald. "Matricially free random variables." Journal of Functional Analysis 258, no. 12 (2010): 4075–121. http://dx.doi.org/10.1016/j.jfa.2010.03.010.

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36

Berger, Erich. "Comparing sums of independent bounded random variables and sums of Bernoulli random variables." Statistics & Probability Letters 34, no. 3 (1997): 251–58. http://dx.doi.org/10.1016/s0167-7152(96)00188-5.

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37

Jimbo, Shuji, та Akira Maruoka. "On the relationship between ε-biased random variables and ε-dependent random variables". Information Processing Letters 51, № 1 (1994): 17–23. http://dx.doi.org/10.1016/0020-0190(94)00061-1.

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38

Kruglov, V. M. "Weak Compactness of Random Sumsof Independent Random Variables." Theory of Probability & Its Applications 43, no. 2 (1999): 203–20. http://dx.doi.org/10.1137/s0040585x97976830.

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39

Sudakov, V. N. "On distributions of random variables chosen at random." Journal of Mathematical Sciences 88, no. 1 (1998): 106–9. http://dx.doi.org/10.1007/bf02363269.

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40

Wu, Yongfeng, та JiangYan Peng. "Strong convergence for weighted sums of ρ*-mixing random variables". Glasnik Matematicki 49, № 1 (2014): 221–34. http://dx.doi.org/10.3336/gm.49.1.15.

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41

Wu, Yongfeng, and Andrew Rosalsky. "Strong convergence for m-pairwise negatively quadrant dependent random variables." Glasnik Matematicki 50, no. 1 (2015): 245–59. http://dx.doi.org/10.3336/gm.50.1.15.

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42

Kagan, Abram, Colin L. Mallows, Larry A. Shepp, Robert J. Vanderbei, and Yehuda Vardi. "Symmetrization of Binary Random Variables." Bernoulli 5, no. 6 (1999): 1013. http://dx.doi.org/10.2307/3318557.

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43

Wolff, Paweł. "Hypercontractivity of simple random variables." Studia Mathematica 180, no. 3 (2007): 219–36. http://dx.doi.org/10.4064/sm180-3-3.

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44

Móri, T. F., and G. J. Székely. "Representations by uncorrelated random variables." Mathematical Methods of Statistics 26, no. 2 (2017): 149–53. http://dx.doi.org/10.3103/s1066530717020041.

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45

Hou, Yongchao, and Weicai Peng. "DISTANCE BETWEEN UNCERTAIN RANDOM VARIABLES." Mathematical Modelling of Engineering Problems 1, no. 1 (2014): 15–20. http://dx.doi.org/10.18280/mmep.010104.

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46

Gerasimov, M., V. Kruglov, and A. Volodin. "On negatively associated random variables." Lobachevskii Journal of Mathematics 33, no. 1 (2012): 47–55. http://dx.doi.org/10.1134/s1995080212010052.

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47

Rockower, Edward B. "Integral Identities for Random Variables." American Statistician 42, no. 1 (1988): 68. http://dx.doi.org/10.2307/2685265.

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48

Nica, Alexandru, and Roland Speicher. "Commutators of free random variables." Duke Mathematical Journal 92, no. 3 (1998): 553–92. http://dx.doi.org/10.1215/s0012-7094-98-09216-x.

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49

Kachapova, Farida, and Ilias Kachapov. "Students’ misconceptions about random variables." International Journal of Mathematical Education in Science and Technology 43, no. 7 (2012): 963–71. http://dx.doi.org/10.1080/0020739x.2011.644332.

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50

Schwartz, Mark. "Summing subsequences of random variables." Rocky Mountain Journal of Mathematics 17, no. 1 (1987): 115–20. http://dx.doi.org/10.1216/rmj-1987-17-1-115.

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