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Journal articles on the topic 'Discrete random variable'

Author: Grafiati

Published: 28 May 2022

Last updated: 31 July 2025

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1

Yanga, Jinyoung, and Mijeong Kim. "Independence test of a continuous random variable and a discrete random variable." Communications for Statistical Applications and Methods 27, no. 3 (2020): 285–99. http://dx.doi.org/10.29220/csam.2020.27.3.285.

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2

Pratsiovytyi, M., N. Vasylenko, Ya Goncharenko, and I. Lysenko. "TWO-SYMBOL SYSTEM OF ENCODING OF NUMBERS AND DISCRETE DISTRIBUTIONS OF RANDOM VARIABLES." Bukovinian Mathematical Journal 11, no. 2 (2023): 225–35. http://dx.doi.org/10.31861/bmj2023.02.22.

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We consider discrete distributions of random variables, defined by various two-symbol systems of encoding of real numbers (with zero and non-zero redundancy, with one and two bases, in particular with different sings), and study structural, topological, metric, and structurally fractal properties their point spectra. The general criterion for random variable with independent digits of two-symbol representation to have discrete distribution (analog of the P. L’ evi theorem for sum of random series with discretely distributed terms) is proved and properties of its spectrum are described. In the

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3

Yang, Jielin. "The Distribution Function of Random Variable and Extension of Mathematical Expectation." Journal of Physics: Conference Series 3004, no. 1 (2025): 012001. https://doi.org/10.1088/1742-6596/3004/1/012001.

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Abstract This work reveals the existence of non-discrete and non-continuous random variables and discusses specific characteristics of the distribution functions of discrete and continuous random variables. It is constructed to create a class of single random variables that are neither discrete nor continuous. Their distribution functions are compared with those of continuous and discrete random variables. Its qualities are then spoken about. To evaluate the discontinuous points of these random variables, an example is provided. We also examine the process of computing the mathematical expecta

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4

Dhritikesh, Chakrabarty. "Beautiful Multiplicative Property of Geometric Expectation." Partners Universal International Innovation Journal (PUIIJ) 02, no. 02 (2024): 92–98. https://doi.org/10.5281/zenodo.10999414.

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Concepts of geometric expectation and harmonic expectation of random variable were introduced in a recent study with formulating their definitions in the case of discrete random variable. It was thought that geometric expectation might carry some properties. A beautiful multiplicative property of geometric expectation has been derived in this study. The property has been derived in the case of discrete random variable. This article presents derivation of this property of geometric expectation with numerical example.

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5

DONG, YUGE, and AINAN WANG. "A FUZZY RELIABILITY ANALYSIS BASED ON THE TRANSFORMATION BETWEEN DISCRETE FUZZY VARIABLES AND DISCRETE RANDOM VARIABLES." International Journal of Reliability, Quality and Safety Engineering 13, no. 01 (2006): 25–35. http://dx.doi.org/10.1142/s0218539306002070.

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When fuzzy information is taken into consideration in design, it is difficult to analyze the reliability of machine parts because we usually must deal with random information and fuzzy information simultaneously. Therefore, in order to make it easy to analyze fuzzy reliability, this paper proposes the transformation between discrete fuzzy random variable and discrete random variable based on a fuzzy reliability analysis when one of the stress and strength is a discrete fuzzy variable and the other is a discrete random variable. The transformation idea put forwards in this paper can be extended

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6

Nikolov, Nikolai, and Mladen Savov. "Properties and Conjectures Regarding Discrete Renewal Sequences." Mathematics and Informatics 67, no. 2 (2024): 111–18. https://doi.org/10.53656/math2024-2-1-pro.

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In this work we review and derive some elementary properties of the discrete renewal sequences based on a positive, finite and integervalued random variable. Our results consider these sequences as dependent on the probability masses of the underlying random variable. In particular we study the minima and the maxima of these sequences and prove that they are attained for indices of the sequences smaller or equal than the support of the underlying random variable. Noting that the minimum itself is a minimum of multi-variate polynomials we conjecture that one universal polynomial envelopes the m

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Kim, Dae San, Taekyun Kim, Wonjoo Kim, Jongkyum Kwon, and Hyunseok Lee. "Degenerate Moments and Expectation of Monomials." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 3847–55. http://dx.doi.org/10.29020/nybg.ejpam.v17i4.5604.

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The aim of this paper is twofold. Firstly, we obtain expressions of the degenerate moments of a discrete nonnegative integer valued random variable. Secondly, we get an expression for the expectation of any monomial in discrete nonnegative integer-valued random variables.

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8

Okazaki, Hiroyuki, and Yasunari Shidama. "Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables." Formalized Mathematics 18, no. 4 (2010): 213–17. http://dx.doi.org/10.2478/v10037-010-0026-6.

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Probability Measure on Discrete Spaces and Algebra of Real-Valued Random Variables In this article we continue formalizing probability and randomness started in [13], where we formalized some theorems concerning the probability and real-valued random variables. In this paper we formalize the variance of a random variable and prove Chebyshev's inequality. Next we formalize the product probability measure on the Cartesian product of discrete spaces. In the final part of this article we define the algebra of real-valued random variables.

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9

Kunte, Sudhakar, and R. N. Rattihalli. "Uniform Random Variables: Do They Exist in the Subjective Sense ?" Calcutta Statistical Association Bulletin 42, no. 1-2 (1992): 125–28. http://dx.doi.org/10.1177/0008068319920111.

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10

ALWAKEEL, ALI HUSEEN. "ON DISCRETE WEIBULL DISTRIBUTION." Journal of Economics and Administrative Sciences 20, no. 79 (2014): 1–9. http://dx.doi.org/10.33095/jeas.v20i79.1969.

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Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number o

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11

الوكيل, علي عبد الحسين. "ON DISCRETE WEIBULL DISTRIBUTION." Journal of Economics and Administrative Sciences 20, no. 79 (2014): 1. http://dx.doi.org/10.33095/jeas.v20i79.807.

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 Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assume the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables takes on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the n

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12

Makarchuk, O. "ASYMPTOTIC BEHAVIOR OF THE CHARACTERISTIC FUNCTION OF ONE DISTRIBUTION OF THE JESSEN-WINTNER TYPE." Bukovinian Mathematical Journal 11, no. 2 (2023): 173–82. http://dx.doi.org/10.31861/bmj2023.02.17.

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The paper considers a random variable, which is the sum of a pointwise convergent random power series with independent discretely distributed terms that take on integer values. The corresponding random variable is a random variable represented by an s-fraction with a redundant set of digits and is included in the set of distributions of the Jessen-Wintner type. The Lebesgue distribution function of a random variable represented by an s-fraction with a redundant set of digits contains only a discrete or absolutely continuous or singular component. Emphasis in the paper is on the study of the as

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13

Kattumannil, Sudheesh Kumar, and Luisa Tibiletti. "Moment identity for discrete random variable and its applications." Statistics 46, no. 6 (2012): 767–75. http://dx.doi.org/10.1080/02331888.2011.555548.

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14

Trzaskalik, Tadeusz, and Sebastian Sitarz. "Discrete dynamic programming with outcomes in random variable structures." European Journal of Operational Research 177, no. 3 (2007): 1535–48. http://dx.doi.org/10.1016/j.ejor.2005.10.019.

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15

Eryilmaz, Serkan. "Discrete Scan Statistics Generated by Exchangeable Binary Trials." Journal of Applied Probability 47, no. 4 (2010): 1084–92. http://dx.doi.org/10.1239/jap/1294170521.

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Let {Xi}i=1n be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable Sn,m to be the maximum number of 1s within any m consecutive trials in {Xi}i=1n. The random variable Sn,m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {Xi}i=1n consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of Sn,m for 2m ≥ n. These results are also new for independent, identically distribut

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16

Caragiu, Mihai, and Mellita Caragiu. "A RANDOM VARIABLE WITH ZETA FUNCTION CONNECTIONS." Far East Journal of Mathematical Education 27, no. 1 (2025): 21–33. https://doi.org/10.17654/0973563125004.

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We present an example of a particularly simple discrete random variable with surprisingly rich connections with calculus (-series, specifically zeta values, and recursive integral calculations) and combinatorics (the binomial coefficients which will appear alongside the zeta values in the expansion of the moment generating function). We believe that our example could be used in the undergraduate probability class, as a bridge-building experience between probability theory and the traditionally related areas of calculus and combinatorics.

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17

Eryilmaz, Serkan. "Discrete Scan Statistics Generated by Exchangeable Binary Trials." Journal of Applied Probability 47, no. 04 (2010): 1084–92. http://dx.doi.org/10.1017/s0021900200007385.

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Let {X i } i=1 n be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable S n,m to be the maximum number of 1s within any m consecutive trials in {X i } i=1 n . The random variable S n,m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {X i } i=1 n consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of S n,m for 2m ≥ n. These results are also new for independent, ident

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18

Liu, Tongtong. "An exploration to random walk." Applied and Computational Engineering 6, no. 1 (2023): 397–403. http://dx.doi.org/10.54254/2755-2721/6/20230814.

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There is a lot of uncertainty in many things that happen in real life, which leads to many events occurring randomly, and the quantitative description of the relationship between this sequence of random events is the stochastic process. Stochastic process is an important part of Probability. The stochastic process is a set of random variables, which is {Xt} t belongs to the T, The variable t is the parameter known as time, The parameter in a stochastic process are uncertain, each t corresponding to a random variable. T is the parameter set, and is a discrete parameter process when T is a finit

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19

Rojas-Nandayapa, Leonardo, and Wangyue Xie. "Asymptotic tail behaviour of phase-type scale mixture distributions." Annals of Actuarial Science 12, no. 2 (2017): 412–32. http://dx.doi.org/10.1017/s1748499517000136.

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AbstractWe consider phase-type scale mixture distributions which correspond to distributions of a product of two independent random variables: a phase-type random variable Y and a non-negative but otherwise arbitrary random variable S called the scaling random variable. We investigate conditions for such a class of distributions to be either light- or heavy-tailed, we explore subexponentiality and determine their maximum domains of attraction. Particular focus is given to phase-type scale mixture distributions where the scaling random variable S has discrete support – such a class of distribut

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20

Hu, Taizhong, Junchao Yao, and Qingshu Lu. "NONNEGATIVITY OF COVARIANCES BETWEEN FUNCTIONS OF ORDERED RANDOM VARIABLES." Probability in the Engineering and Informational Sciences 21, no. 4 (2007): 557–77. http://dx.doi.org/10.1017/s0269964807000320.

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In this article we investigate conditions by a unified method under which the covariances of functions of two adjacent ordered random variables are nonnegative. The main structural results are applied to several kinds of ordered random variable, such as delayed record values, continuous and discrete ℓ∞⩽-spherical order statistics, epoch times of mixed Poisson processes, generalized order statistics, discrete weak record values, and epoch times of modified geometric processes. These applications extend the main results for ordinary order statistics in Qi [28] and for usual record values in Naga

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21

Deng, Changbao, Weinuo Jiang, and Shihong Wang. "Detecting interactions in discrete-time dynamics by random variable resetting." Chaos: An Interdisciplinary Journal of Nonlinear Science 31, no. 3 (2021): 033146. http://dx.doi.org/10.1063/5.0028411.

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22

Deshpande, M. N. "85.76 Another Discrete Random Variable Having the Property 'Mean = Variance'." Mathematical Gazette 85, no. 504 (2001): 516. http://dx.doi.org/10.2307/3621778.

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23

Prasanta Kumar Das. "On Discrete Harmonic Distributions related with Harmonic Mean Random Variable." Communications on Applied Nonlinear Analysis 31, no. 8s (2024): 565–73. http://dx.doi.org/10.52783/cana.v31.1549.

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The main purpose of this paper is to introduce the concept of harmonically distributed discrete random variable. We define probability mass function such as harmonic mass function, exponential harmonic mass function, natural logarithmic harmonic mass function and their associated cumulative distribution functions. Existence the distribution is shown with some examples. Finally harmonic mass function is used to solve a run-time problem and a capacitance problem as an application of the distribution in the field of electrical engineering.

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24

Borghesani, P., P. Pennacchi, R. B. Randall, and R. Ricci. "Order tracking for discrete-random separation in variable speed conditions." Mechanical Systems and Signal Processing 30 (July 2012): 1–22. http://dx.doi.org/10.1016/j.ymssp.2012.01.015.

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25

Veres-Ferrer, Ernesto J., and Jose M. Pavía. "Elasticity function of a discrete random variable and its properties." Communications in Statistics - Theory and Methods 46, no. 17 (2017): 8631–46. http://dx.doi.org/10.1080/03610926.2016.1186190.

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26

Wu, Guo-Cheng, Dumitru Baleanu, He-Ping Xie, and Sheng-Da Zeng. "Discrete Fractional Diffusion Equation of Chaotic Order." International Journal of Bifurcation and Chaos 26, no. 01 (2016): 1650013. http://dx.doi.org/10.1142/s0218127416500139.

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Discrete fractional calculus is suggested in diffusion modeling in porous media. A variable-order fractional diffusion equation is proposed on discrete time scales. A function of the variable order is constructed by a chaotic map. The model shows some new random behaviors in comparison with other variable-order cases.

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27

Bening, Vladimir E., and Victor Y. Korolev. "Comparing Distributions of Sums of Random Variables by Deficiency: Discrete Case." Mathematics 10, no. 3 (2022): 454. http://dx.doi.org/10.3390/math10030454.

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In the paper, we consider a new approach to the comparison of the distributions of sums of random variables. Unlike preceding works, for this purpose we use the notion of deficiency that is well known in mathematical statistics. This approach is used, first, to determine the distribution of a separate random variable in the sum that provides the least possible number of summands guaranteeing the prescribed value of the (1−α)-quantile of the normalized sum for a given α∈(0,1), and second, to determine the distribution of a separate random variable in the sum that provides the least possible num

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28

Szabados, Tamás, and Balázs Székely. "An exponential functional of random walks." Journal of Applied Probability 40, no. 2 (2003): 413–26. http://dx.doi.org/10.1239/jap/1053003553.

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The aim of this paper is to investigate discrete approximations of the exponential functional of Brownian motion (which plays an important role in Asian options of financial mathematics) with the help of simple, symmetric random walks. In some applications the discrete model could be even more natural than the continuous one. The properties of the discrete exponential functional are rather different from the continuous one: typically its distribution is singular with respect to Lebesgue measure, all of its positive integer moments are finite and they characterize the distribution. On the other

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29

Szabados, Tamás, and Balázs Székely. "An exponential functional of random walks." Journal of Applied Probability 40, no. 02 (2003): 413–26. http://dx.doi.org/10.1017/s0021900200019392.

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The aim of this paper is to investigate discrete approximations of the exponential functional of Brownian motion (which plays an important role in Asian options of financial mathematics) with the help of simple, symmetric random walks. In some applications the discrete model could be even more natural than the continuous one. The properties of the discrete exponential functional are rather different from the continuous one: typically its distribution is singular with respect to Lebesgue measure, all of its positive integer moments are finite and they characterize the distribution. On the other

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30

Li, Wenhan, Wei Wang, and Zhiqiang Liu. "Likelihood Ratio and Strong Limit Theorems for the Discrete Random Variable." Open Journal of Discrete Mathematics 02, no. 04 (2012): 169–72. http://dx.doi.org/10.4236/ojdm.2012.24034.

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31

Cuchta, Tom, and Robert J. Niichel. "Memoryless Properties on Time Scales." Mathematica Slovaca 73, no. 4 (2023): 911–20. http://dx.doi.org/10.1515/ms-2023-0067.

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ABSTRACT The classical memoryless property is well-known to induce the geometric distribution for discrete random variables and the exponential distribution for continuous random variables. When the range of the random variable is just an arbitrary closed subset of the real line, significant difficulties arise as to the interpretation of the memoryless property itself. Multiple proposals have been made, and we explore their consequences. In particular, we consider whether a given definition of “memoryless” will induce a specific distribution.

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32

Kim, Hye Kyung. "Fully degenerate Bell polynomials associated with degenerate Poisson random variables." Open Mathematics 19, no. 1 (2021): 284–96. http://dx.doi.org/10.1515/math-2021-0022.

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Abstract Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al. studied the degenerate gamma random variables, discrete degenerate random variables and two-variable degenerate Bell polynomials associated with Poisson degenerate central moments, etc. This paper is divided into two parts. In the first part, we introduce a new type of degenerate Bell polynomials associated with degenerate Poisson random variables with parameter α > 0 \alpha \hspace{-0.15em}\gt \hspace{-0.15

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33

Meštrović, Romeo. "On Some Compound Random Variables Motivated by Bulk Queues." Mathematical Problems in Engineering 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/291402.

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We consider the distribution of the number of customers that arrive in an arbitrary bulk arrival queue system. Under certain conditions on the distributions of the time of arrival of an arriving group (Y(t)) and its size (X) with respect to the considered bulk queue, we derive a general expression for the probability mass function of the random variableQ(t)which expresses the number of customers that arrive in this bulk queue during any considered periodt. Notice thatQ(t)can be considered as a well-known compound random variable. Using this expression, without the use of generating function, w

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34

Zhang, Ji Cheng, and Jun Yang. "Reliability Analysis on Construction Course of Open Caisson Structure." Applied Mechanics and Materials 166-169 (May 2012): 1976–80. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.1976.

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The numerical model was established using ANSYS software, which took the interaction effect of subsoil and structure into account, the soil was considered as discrete spring elements. The soil’s mechanic parameters were set as random variable, probability analysis was performed on typical construction course of open caisson by Monte-Carlo method, the distribution rule of displacement random variables and their sensitivity to variable factors were studied, and the influence of uncertain factors on open caisson’s sinking attitude was investigated. The analysis model showed good practical value f

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35

Satheesh, S., and N. Unnikrishnan Nair. "A Note on Maximum and Minimum Stability of Certain Distributions." Calcutta Statistical Association Bulletin 53, no. 3-4 (2002): 249–52. http://dx.doi.org/10.1177/0008068320020308.

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36

Brown, Timothy C. "Transforming a random variable to a prescribed distribution: an application to school-based assessment." Journal of Applied Probability 41, A (2004): 239–52. http://dx.doi.org/10.1239/jap/1082552202.

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When can one find a smooth transformation of a random variable so that the transformed random variable has a specified distribution? If the random variable is continuous, the solution is elementary; if it is discrete, it may be impossible. In this paper, a simple method is given of transforming a random variable in a smooth way to match a specified number of quantiles of an arbitrary distribution. The problem arose from a request for a simple way of transforming marks given in school assessment so that the distribution of transformed marks matches the distribution of external assessment.

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Brown, Timothy C. "Transforming a random variable to a prescribed distribution: an application to school-based assessment." Journal of Applied Probability 41, A (2004): 239–52. http://dx.doi.org/10.1017/s002190020011232x.

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When can one find a smooth transformation of a random variable so that the transformed random variable has a specified distribution? If the random variable is continuous, the solution is elementary; if it is discrete, it may be impossible. In this paper, a simple method is given of transforming a random variable in a smooth way to match a specified number of quantiles of an arbitrary distribution. The problem arose from a request for a simple way of transforming marks given in school assessment so that the distribution of transformed marks matches the distribution of external assessment.

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38

Habibi, S. R., and R. Burton. "The Variable Structure Filter." Journal of Dynamic Systems, Measurement, and Control 125, no. 3 (2003): 287–93. http://dx.doi.org/10.1115/1.1590682.

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This paper presents a new strategy for state estimation. The strategy may be applied to linear systems and is referred to as the variable structure filter. The filter is considered for discrete-time systems subject to random disturbances and measurement noise. It requires a parametric model and can be formulated to accommodate modeling uncertainties. A proof of stability for the filter is provided. For stability, this concept requires a specification of an upper bound for uncertainties, disturbances, and measurement noise. The application of this filter to a third-order linear system is demons

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39

Kajiwara, Tsuyoshi. "Fourier inversion formula for discrete nilpotent groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 46, no. 3 (1989): 415–22. http://dx.doi.org/10.1017/s1446788700030901.

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AbstractLet G be a countable torsion free finitely generated nilpotent group. Then the Fourier transform can be considered as a map from the space of bounded degree 1 random operators to the Fourier algebra A(G). In this paper, we recover the matrix elements of a positive random variable from the corresponding positive definite function in A(G) for such a group.

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40

Dhritikesh, Chakrabarty. "Additive Property of Harmonic Expectation From That of Arithmetic Expectation." Partners Universal International Innovation Journal (PUIIJ) 02, no. 06 (2024): 24–30. https://doi.org/10.5281/zenodo.14629929.

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An additive property of harmonic expectation was derived in the case of discrete random variable from the classical definition of harmonic expectation. Here, the same has been derived from the additive property of arithmetic expectation. This derivation of the additive property of harmonic expectation, along with numerical example, has been presented in this article.

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41

Lewbel, Arthur. "Semiparametric Estimation of Location and Other Discrete Choice Moments." Econometric Theory 13, no. 1 (1997): 32–51. http://dx.doi.org/10.1017/s0266466600005636.

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Latent variable discrete choice model estimation and interpretation depend on the density function of the latent variable's unobserved random component. This paper provides a simple semiparametric estimator of the moments of this density. The results can be used as starting values for parametric estimators, to estimate the appropriate location and scaling for semiparametric estimators, for specification testing including tests of latent error skewness and kurtosis, and to estimate coefficients of discrete explanatory variables in the model.

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42

Pratsiovytyi, Mykola, Iryna Lysenko, and Oksana Voitovska. "Distribution of values of classic singular Cantor function of random argument." Random Operators and Stochastic Equations 26, no. 4 (2018): 193–200. http://dx.doi.org/10.1515/rose-2018-0016.

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Abstract Let X be a random variable with independent ternary digits and let {y=F(x)} be a classic singular Cantor function. For the distribution of the random variable {Y=F(X)} , the Lebesgue structure (i.e., the content of discrete, absolutely continuous and singular components), the structure of its point and the continuous spectra are exhaustively studied.

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43

Xiao, Sheng-xie, and En-lin Lü. "Mathematical expectation about discrete random variable with interval probability or fuzzy probability." Applied Mathematics and Mechanics 26, no. 10 (2005): 1382–90. http://dx.doi.org/10.1007/bf03246243.

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44

Zakharov, V. M., S. V. Shalagin, and A. I. Gumirov. "Discrete Random Variable Generator With the Given Distribution Law in FPGA-Architecture." Herald of Dagestan State University 38, no. 3 (2023): 28–33. http://dx.doi.org/10.21779/2542-0321-2023-38-3-28-33.

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45

Kolchinsky, Artemy, Brendan D. Tracey, and David H. Wolpert. "Nonlinear Information Bottleneck." Entropy 21, no. 12 (2019): 1181. http://dx.doi.org/10.3390/e21121181.

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Information bottleneck (IB) is a technique for extracting information in one random variable X that is relevant for predicting another random variable Y. IB works by encoding X in a compressed “bottleneck” random variable M from which Y can be accurately decoded. However, finding the optimal bottleneck variable involves a difficult optimization problem, which until recently has been considered for only two limited cases: discrete X and Y with small state spaces, and continuous X and Y with a Gaussian joint distribution (in which case optimal encoding and decoding maps are linear). We propose a

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46

Lapko, A. V., and V. A. Lapko. "Estimation of traditional numerical characteristics of lognormal distribution laws of a one-dimensional random variable in conditions of large volume statistical data." Izmeritel`naya Tekhnika, no. 2 (April 5, 2024): 23–29. http://dx.doi.org/10.32446/0368-1025it.2024-2-23-29.

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The efficiency of estimating the numerical characteristics of a family of the lognormal distribution law of a onedimensional random variable under conditions of large volumes of statistical data is considered. To circumvent the problem of large samples, methods of discretization the range of values of a random variable based on the formulas of Sturges, Brooks-Carruthers, Heinhold-Gaede and the formula proposed by the authors of this article are used. Data arrays have been generated that make it possible to evaluate the numerical characteristics of the laws of distribution of random variables,

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Padoan, Alberto; Astolfi Alessandro. "Moments of Random Variables: A Systems-Theoretic Interpretation." IEEE Transactions on Automatic Control 64, no. 11 (2019): 4407–22. https://doi.org/10.1109/TAC.2019.2898167.

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Moments of continuous random variables admitting a probability density function are studied. We show that, under certain assumptions, the moments of a random variable can be characterized in terms of a Sylvester equation and of the steady-state output response of a specific interconnected system. This allows to interpret well-known notions and results of probability theory and statistics in the language of systems theory, including the sum of independent random variables, the notion of mixture distribution and results from renewal theory. The theory developed is based on tools from center mani

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Malakar, Indra. "Theorizing Probability Distribution in Applied Statistics." Journal of Population and Development 1, no. 1 (2020): 79–95. http://dx.doi.org/10.3126/jpd.v1i1.33107.

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This paper investigates into theoretical knowledge on probability distribution and the application of binomial, poisson and normal distribution. Binomial distribution is widely used discrete random variable when the trails are repeated under identical condition for fixed number of times and when there are only two possible outcomes whereas poisson distribution is for discrete random variable for which the probability of occurrence of an event is small and the total number of possible cases is very large and normal distribution is limiting form of binomial distribution and used when the number

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Calik, Sinan, and Ayse Bugatekin. "Moments of sample extremes of order statistics from discrete uniform distribution and numerical results." Thermal Science 22, Suppl. 1 (2018): 237–41. http://dx.doi.org/10.2298/tsci170612291c.

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In this study, the mth raw moments of sample extremes of order statistics from discrete uniform distribution are obtained. The results of sample extremes of order statistics of random variable for the independent and identically discrete uniform distribution are given. Numerical values are shown in table form

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50

Sason, Igal. "Tight Bounds on the Rényi Entropy via Majorization with Applications to Guessing and Compression." Entropy 20, no. 12 (2018): 896. http://dx.doi.org/10.3390/e20120896.

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This paper provides tight bounds on the Rényi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one to one. To that end, a tight lower bound on the Rényi entropy of a discrete random variable with a finite support is derived as a function of the size of the support, and the ratio of the maximal to minimal probability masses. This work was inspired by the recently published paper by Cicalese et al., which is focused on the Shannon entropy, and it strengthens and generalizes the results of that paper to Rényi entropi

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