Relevant bibliographies by topics / Product of independent random variables

Contents

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

Academic literature on the topic 'Product of independent random variables'

Author: Grafiati
Published: 4 June 2021
Last updated: 15 February 2022

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Journal articles on the topic "Product of independent random variables"

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Dettmann, Carl P., and Orestis Georgiou. "Product of independent uniform random variables." Statistics & Probability Letters 79, no. 24 (December 2009): 2501–3. http://dx.doi.org/10.1016/j.spl.2009.09.004.

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Cline, D. B. H., and G. Samorodnitsky. "Subexponentiality of the product of independent random variables." Stochastic Processes and their Applications 49, no. 1 (January 1994): 75–98. http://dx.doi.org/10.1016/0304-4149(94)90113-9.

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Jovanovic Dolecek, Gordana. "Teaching Random Variables." U.Porto Journal of Engineering 7, no. 1 (February 19, 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 satisfied with this demo program expressing that helped them understanding better the behaviour of the product of uniform random variables.
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Salo, J., H. M. El-Sallabi, and P. Vainikainen. "The Distribution of the Product of Independent Rayleigh Random Variables." IEEE Transactions on Antennas and Propagation 54, no. 2 (February 2006): 639–43. http://dx.doi.org/10.1109/tap.2005.863087.

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Sato, Hiroshi. "On the convergence of the product of independent random variables." Journal of Mathematics of Kyoto University 27, no. 2 (1987): 381–85. http://dx.doi.org/10.1215/kjm/1250520722.

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Behboodian, J. "Symmetric sum and symmetric product of two independent random variables." Journal of Theoretical Probability 2, no. 2 (April 1989): 267–70. http://dx.doi.org/10.1007/bf01053413.

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Su, Chun, and Yu Chen. "On the behavior of the product of independent random variables." Science in China Series A 49, no. 3 (January 2006): 342–59. http://dx.doi.org/10.1007/s11425-006-0342-z.

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Nadarajah, Saralees, and Arjun K. Gupta. "On the product and ratio of Bessel random variables." International Journal of Mathematics and Mathematical Sciences 2005, no. 18 (2005): 2977–89. http://dx.doi.org/10.1155/ijmms.2005.2977.

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The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product|XY|and the ratio|X/Y|are derived whenXandYare independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.
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Hall, Peter, and Eugene Seneta. "Products of independent, normally attracted random variables." Probability Theory and Related Fields 78, no. 1 (1988): 135–42. http://dx.doi.org/10.1007/bf00718041.

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Abramov, V. A. "Convergence of products of independent random variables." Journal of Soviet Mathematics 35, no. 2 (October 1986): 2293–301. http://dx.doi.org/10.1007/bf01105645.

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Dissertations / Theses on the topic "Product of independent random variables"

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Kasparavičiūtė, Aurelija. "Theorems of large deviations for the sums of a random number of independent random variables." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20140121_101308-41106.

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The research object of this thesis is the sum of a random number of summands of independent identically distributed random variables with positive weights. Such sums appear as models, for example, in insurance, finance mathematics. Throughout the thesis, it is assumed that the random number of summands is independent of the summands, the summands satisfy S. N. Bernstein's condition, and the random number of summands together with weights satisfy some compatibility conditions. The aim of this dissertation is a normal approximation to a distribution of the sum of a random number of summands of independent identically distributed random variables with positive weights that takes into consideration large deviations in both the Cramer and the power Linnik zones.
Disertacinio darbo tyrimo objektas yra atsitiktinio dėmenų skaičiaus nepriklausomų vienodai pasiskirsčiusių atsitiktinių dydžių su teigiamais svoriniais koeficientais sumos, kurios kaip modelis sutinkamos, pavyzdžiui, finansų, draudos matematikose. Daromos prielaidos, kad atsitiktinis dėmenų skaičius yra nepriklausomas nuo sumos dėmenų, atsitiktiniai dėmenys tenkina apibendrintą S. N. Bernšteino sąlygą, o atsitiktinis dėmenų skaičius kartu su svoriais tenkina tam tikras suderinamumo sąlygas. Disertacijos tikslas yra standartizuotos (centruotos ir normuotos) minėtos atsitiktinės sumos skirstinio aproksimacija standartiniu normaliuoju dėsniu didžiųjų nuokrypių tiek Kramero, tiek ir laipsninėse Liniko zonose.
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Sambale, Holger [Verfasser]. "Second order concentration for functions of independent random variables / Holger Sambale." Bielefeld : Universitätsbibliothek Bielefeld, 2016. http://d-nb.info/1084888173/34.

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Wu, Hao-cun. "Independent component analysis and its applications in finance." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39559099.

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吳浩存 and Hao-cun Wu. "Independent component analysis and its applications in finance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39559099.

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Baumgarten, Christoph [Verfasser], and Frank [Akademischer Betreuer] Aurzada. "Persistence of sums of independent random variables, iterated processes and fractional Brownian motion / Christoph Baumgarten. Betreuer: Frank Aurzada." Berlin : Universitätsbibliothek der Technischen Universität Berlin, 2013. http://d-nb.info/1035276445/34.

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Staskevičiūtė, Simona. "Atsitiktinių dydžių sandaugų tikimybiniai skirstiniai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2013. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2013~D_20130617_182710-60131.

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Magistro baigiamajame darbe analizuojami matematinės statistikos tikimybiniai skirstiniai. Darbo tikslas – atlikti nepriklausomų beta atsitiktinių dydžių sandaugos pasiskirstymo analizę. Ši tematika aktuali sudėtingų sistemų patikimumo analizės teorijoje. Darbe aprašyta neaprėžtai dalių tikimybinių skirstinių teorija, kuri naudojama atsitiktinių dydžių sumos pasiskirstymui tirti, ir M-dalių tikimybių pasiskirstymo modelių teorija, naudojama nepriklausomų atsitiktinių dydžių sandaugos pasiskirstymo analizei atlikti. Baigiamajame darbe suformuluotos dvi teoremos, nusakančios, kuriais atvejais daugindami baigtinį skaičių nepriklausomų beta atsitiktinių dydžių su skirtingomis parametrų reikšmėmis gauname beta atsitiktinį dydį, kurio parametrai išreikšti per dauginamųjų parametrus. Šios teoremos įrodytos, kuomet dauginame du nepriklausomus beta atsitiktinius dydžius. Taip pat darbe suformuluota ir įrodyta teorema, nurodanti beta atsitiktinio dydžio logaritmo charakteringosios funkcijos analitinę išraišką.
The mathematical statistics probability distributions are analyzed in this master thesis. The main purpose is to carry out the analysis of independent beta random variables products distribution. This theme is relevant to the reliability analysis of complex systems theory. The theoretics of unlimited divisible probability distributions is described in this master thesis. Following theory is useful to investigate the sums of independent random variables. The theoretics of M-divisible probability distributions is also described in this master thesis. It is useful to investigate the product of independent random variables. Two theorems about the product of finite number of independent beta random variables are formulated in this master thesis. Following theorems tells us, that product is beta random variable again, and its parameters expressions are related with multiplicands parameters. Theorems are proved when we are multiplying two independent beta random variables. Another theorem that is about characteristic function of beta random variable logarithm is formulated and proved in this master thesis.
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Paditz, Ludwig. "Über die Annäherung von Summenverteilungsfunktionen gegen unbegrenzt teilbare Verteilungsfunktionen in der Terminologie der Pseudomomente." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112967.

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Die Pseudomomente dienen als Charakteristikum der Annäherung der Komponenten einer Summenverteilungsfunktion gegen die Komponenten der Grenzverteilungsfunktion. In der Terminologie der Pseudomomente werden Abschätzungen der Annäherung der Summenverteilungsfunktion gegen eine unbegrenz teilbare Verteilungsfunktion angegeben. Dabei werden die Aussagen ohne die Voraussetzung der sogenannten Infinitesimalitätsbedingung hergeleitet. Es werden Abschätzungen angegeben sowohl unter der Voraussetzung endlicher Streuungen als auch ohne diese Voraussetzung. Abschließend werden einige Literaturhinweise angegeben
The pseudo-moments serve as a characteristic of the approach of the components of a cumulative distribution function to the components of the limit distribution function. In the terminology of pseudo-moments estimates of the approximation of the cumulative distribution function by an indefinite divisible distribution function can be specified. The results are derived without the assumption of the so-called condition of infinitesimality. There are given some estimations with or without the assumption of finite variances. Finally some references are given
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Halconruy, Hélène. "Calcul de Malliavin et structures de Dirichlet pour des variables aléatoires indépendantes." Electronic Thesis or Diss., Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAT016.

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Cette thèse porte sur le calcul de Malliavin dont on munit deux cadres discrets. On équipe tout produit dénombrable d'espaces de probabilités d'une structure de Dirichlet-Malliavin au moyen d'opérateurs (gradient, divergence, opérateur nombre), d'une formule d'intégration par parties, et des formes de Dirichlet induites. On obtient les analogues discrets aux identités fonctionnelles classiques des processus Brownien et Poisson dont les structures de Dirichlet s'écrivent comme limites des structures induites par notre formalisme. Des critères de Stein-Malliavin discrets sont établis pour les approximations Normale et Gamma. Le second cadre est celui d'un modèle financier ternaire sous-tendu par un processus géométrique composé à trois points, et équivalent en loi au modèle trinomial. Toute fonctionnelle de ce processus géométrique composé de carré intégrable possède un développement en chaos "modifié" sur lequel agissent des opérateurs d'annihilation/gradient et de création/divergence vérifiant en outre une formule de commutation généralisée. S'ensuit de la formulede Clark "géométrique" qu'il est alors possible d'établir, une formule de hedging pour l'initié dont l'utilité additionnelle espérée s'exprime en termes d'entropie relative, comme dans le cas continu
Malliavin calculus was initially developed to provide an infinite-dimensional variational calculus on the Wiener space and further extended to other spaces. In this work, we develop such one in two discrete frameworks. First, we equip any countable product of probability spaces with a discrete Dirichlet-Malliavin structure, consisting of a family of Malliavin operators (gradient, divergence, number operator), an integration by parts formula, and the induced Dirichlet forms. We get the analogues of the classical functional identities and retrieve the usual Poisson and Brownian Dirichlet structures as limits of our induced structures. We provide discrete Stein-Malliavin criterions for the Normal and the Gamma approximations. Second we study insider's trading in a ternary model, Iying on a three-points compound geometric process. We state a modified chaotic decomposition and define the geometric gradient and divergence operators as the annihilation and creation operators acting on it. We state a geometric Ocone-Karatzas formula. We express the insider's additional expected logarithmic utility in terms of relative entropy as in the continuous case
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Bacro, Jean-Noël. "Sur les accroissements des processus de sommes partielles de variables aléatoires indépendantes." Paris 6, 1986. http://www.theses.fr/1986PA066372.

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Considérant une suite de variables aléatoires non-dégénérées, indépendantes et de même loi, on s'intéresse au maximum des suites de sommes partielles pour des incréments dont la longueur est la partie entière de l'expression c log(n) + d log(log(n)), ou log désigne la fonction logarithme, c une constante strictement positive, d’une constante réelle et n la taille de l'échantillon. Ce genre de problème est directement lié aux lois de type Erdoes-Renyi-Shepp. A l'aide d'un théorème de grande déviation, nous montrons comment se comportent la limite en probabilité et les limites inferieures et supérieures presque sûres de la différence entre le maximum concerne et sa limite presque sure, en fonction de d. Les résultats obtenus sont alors appliqués à un processus de renouvellement et permettent de mettre en évidence la vitesse de convergence optimale du maximum et du minimum du processus pour des accroissements de type Erdoes-Renyi; le cas particulier du processus de poisson standard est explicite. Pour finir, considérant le cas particulier ou les variables aléatoires sont indépendantes, de loi normale centrée réduite, on donne des bornes inferieures et supérieures de la distribution limite de la statistique de Shepp. Conformément aux résultats précédents, il apparait que le maximum de Shepp a un comportement limite en loi de nature oscillante, proche d'une loi de Gumel.
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Paditz, Ludwig. "Über mittlere Abweichungen." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-112977.

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In diesem Artikel werden notwendige und hinreichende Bedingungen für die Gültigkeit von Grenzwertsätzen für mittlere Abweichungen untersucht. In der Terminilogie von J.V.LINNIK (1971) werden die x-Bereiche für mittlere Abweichungen gewöhnlich als "sehr enge" Zonen der integralen normalen Anziehung bezeichnet. Darüber hinaus werden die Restglieder untersucht, die in den asymptotischen Beziehungen auftreten. Die Ordnung der Konvergenzgeschwindigkeit wird angegeben. Frühere Ergebnisse einiger Autoren werden verallgemeinert. Abschließend werden einige Literaturhinweise angegeben
In this paper we study necessary and sufficient conditions for the validity of limit theorems on moderate deviations. Usually x-zones for moderate deviations are called in the terminilogy by YU.V.LINNIK (1971) "very narrow" zones of integral normal attraction. Moreover we analyse the remainder term appearing in the asymptotic relations. Informations on the order of the rate of convergence are given. Earlier results by several authors are generalized. Finally some references are given
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Books on the topic "Product of independent random variables"

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Braverman, Michael Sh. Independent random variables and rearrangement invariant spaces. Cambridge: Cambridge University Press, 1994.

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Arak, T. V. Uniform limit theorems for sums of independent random variables. Providence, R.I: American Mathematical Society, 1988.

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Petrov, V. V. Limit theorems of probability theory: Sequences of independent random variables. Oxford: Clarendon Press, 1995.

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Meerschaert, Mark M. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. New York, USA: John Wiley & Sons, 2001.

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Random walk and the heat equation. Providence, R.I: American Mathematical Society, 2010.

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Lemeshko, Boris, and Irina Veretel'nikova. Criteria for testing hypotheses about randomness and the absence of a trend. Application Guide. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1587437.

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The monograph discusses the application of statistical criteria aimed at testing hypotheses about the absence of a trend in the analyzed samples. The rejection of such a hypothesis gives grounds to consider the analyzed data as samples of independent equally distributed random variables. We consider a set of special criteria aimed at testing such hypotheses, as well as a set of criteria for the uniformity of laws, the uniformity of averages and the uniformity of variances, which can also be used for these purposes. The disadvantages and advantages of various criteria are emphasized, the application of criteria in conditions of violation of standard assumptions is considered. Estimates of the power of the criteria are given, which allows you to navigate when choosing the most preferred criteria. Following the recommendations will ensure the correctness and increase the validity of statistical conclusions when analyzing data. It is intended for specialists who are interested in the application of statistical methods for the analysis of various aspects and trends of the surrounding reality and who are in contact with the processing of experimental results, the need for data analysis in their activities. It will be useful for engineers, researchers, specialists of various profiles (doctors, biologists, sociologists, economists, etc.) who face the need for statistical analysis of experimental results in their activities. It will also be useful for university teachers, graduate students and students.
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Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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Brown, A. A., and V. V. Petrov. Sums of Independent Random Variables. Springer, 2011.

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Sums of Independent Random Variables. Springer, 2011.

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Korolev, V. Y., and V. M. Zolotarev. Limit Distributions for Sums of Independent Random Variables. Brill Academic Pub, 2007.

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Book chapters on the topic "Product of independent random variables"

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Shimura, Takaaki. "The Product of Independent Random Variables with Regularly Varying Tails." In Recent Developments in Infinite-Dimensional Analysis and Quantum Probability, 411–32. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0842-6_29.

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Marques, Filipe J., Indranil Ghosh, Johan Ferreira, and Andriëtte Bekker. "A Note on the Product of Independent Beta Random Variables." In Advances in Statistics - Theory and Applications, 69–83. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62900-7_4.

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Marques, Filipe J. "Gamma-Series Representations for the Sum of Independent Gamma Random Variables and for the Product of Independent Beta Random Variables." In Contributions to Statistics, 241–53. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76605-8_17.

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Coelho, Carlos A., and Rui P. Alberto. "On the Distribution of the Product of Independent Beta Random Variables — Applications." In Advances in Statistics - Theory and Applications, 85–117. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-62900-7_5.

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Coelho, Carlos A., and Barry C. Arnold. "Multiple Products of Independent Beta Random Variables with Finite Form Representations for Their Distributions." In Finite Form Representations for Meijer G and Fox H Functions, 19–27. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-28790-0_3.

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Gooch, Jan W. "Independent Random Variables." In Encyclopedic Dictionary of Polymers, 983. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_15255.

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Jacod, Jean, and Philip Protter. "Independent Random Variables." In Universitext, 61–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-51431-9_10.

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Jacod, Jean, and Philip Protter. "Independent Random Variables." In Universitext, 65–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-642-55682-1_10.

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Catalano, Costanza, and Alberto Gandolfi. "Partially Independent Random Variables." In Springer Proceedings in Mathematics & Statistics, 33–56. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-46310-0_3.

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Chow, Yuan Shih, and Henry Teicher. "Sums of Independent Random Variables." In Springer Texts in Statistics, 113–64. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1950-7_5.

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Conference papers on the topic "Product of independent random variables"

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Tsallis, Constantino, Sílvio M. Duarte Queirós, Sumiyoshi Abe, Hans Herrmann, Piero Quarati, Andrea Rapisarda, and Constantino Tsallis. "Nonextensive statistical mechanics and central limit theorems I—Convolution of independent random variables and q-product." In COMPLEXITY, METASTABILITY, AND NONEXTENSIVITY: An International Conference. AIP, 2007. http://dx.doi.org/10.1063/1.2828765.

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Brilhante, M. Fátima, M. Ivette Gomes, and Dinis Pestana. "Further results on order statistics and products of functions of independent generalized beta random variables." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912748.

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Coelho, Carlos A., and Barry C. Arnold. "Instances of the product of independent beta random variables and of the Meijer G and Fox H functions with finite representations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756348.

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Xi, Zhimin, Byeng D. Youn, and Chao Hu. "Effective Random Field Characterization Considering Statistical Dependence for Probability Analysis and Design." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29183.

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The Proper Orthogonal Decomposition (POD) method has been employed to extract the important signatures of the random field presented in an engineering product or process. Our preliminary study found that coefficients of the signatures are statistically uncorrelated but may be dependent. In general, the statistical dependence of the coefficients is ignored in the random field characterization for probability analysis and design. This paper thus proposes an effective approach to characterize the random field for probability analysis and design while accounting for the statistical dependence among the coefficients. The proposed approach is composed of two technical contributions. The first contribution is to develop a generic approximation scheme of random field as a function of the most important field signatures while preserving prescribed approximation accuracy. The coefficients of the signatures can be modeled as random field variables and their statistical properties are identified using the Chi-Square goodness-of-fit test. Second, the Rosenblatt transformation is employed to transform the statistically dependent random field variables into statistically independent random field variables. There exist so many transformation sequences when the number of random field variables becomes large. It was found that an improper selection of a transformation sequence may introduce high nonlinearity into system responses, which causes inaccuracy in probability analysis and design. Hence, a novel procedure is proposed for determining an optimal transformation sequence that introduces the least degree of nonlinearity to the system response after the Rosenblatt transformation. The proposed random field characterization can be integrated with one of the advanced probability analysis methods, such as the Eigenvector Dimension Reduction (EDR) method, Polynomial Chaos Expansion (PCE) method, etc. Three structural examples including a Micro-Electro-Mechanical Systems (MEMS) bistable mechanism are used to demonstrate the effectiveness of the proposed approach. The results show that the statistical dependence in random field characterization cannot be neglected for probability analysis and design. Moreover, it is shown that the proposed random field approach is very accurate and efficient.
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Vadde, Srikanth, Sagar Kamarthi, and Ibrahim Zeid. "Pricing Remanufactured Products Under Stochastic Demand and Backlogging." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49943.

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Independent and small scale product recovery facilities (PRFs) often struggle to achieve profits under inconsistent inflows of discarded products and varying demand patterns for remanufactured products. Inconsistent inflows coupled with the varying demand cause undue fluctuations in inventory levels and holding costs. PRFs can leverage the inventory levels by posting appropriate prices for remanufactured products and procuring the right quantity of discarded products. This work determines the optimal prices of remanufactured products and the optimal procurement quantity of discarded products when (a) PRFs passively accept and proactively acquire discarded products, (b) demand for remanufactured products is stochastic, and (c) backlogging of demand is permitted. The stochastic demand is modeled to consist of an additive random variable. Optimal solutions are established when the additive random variable follows a generic probability distribution.
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Xi, Zhimin, and Byeng D. Youn. "An Effective Random Field Characterization for Probability Analysis and Design." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49481.

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So far manufacturing tolerance variability over samples has been widely considered in many engineering design problems. Traditionally the tolerance variability is modeled as a spatially independent random parameter although the variability is a function of spatial variables (x, y, and z) in many engineering applications. Little attention has been paid to spatial variability (or random field) in manufacturing and operational conditions, which may dominantly affect system performances in smaller scale applications. This paper presents an effective approach to characterize a random field for probability analysis and design. The Proper Orthogonal Decomposition (POD) method is employed to extract the important signatures of the random field over product samples. A normalized posteriori error is defined to automatically decide the minimal number of the important signatures while preserving a prescribed accuracy in approximating the random field. The random projected values of the spatial variability over the samples onto each important signature are modeled as a random parameter. The signatures and corresponding random parameters are thus used for modeling the random field. A Chi-Squae goodness-of-fit test is used for determining statistical models of random parameters. This proposed approach can facilitate to characterize the random field for probability analysis and design. By modeling the random field with the most significant random signatures, the Eigenvector Dimension Reduction (EDR) method can be employed for probability analysis because of its relatively high efficiency and accuracy. Two examples (one beam and Micro-Electro-Mechanical Systems (MEMS) bistable mechanism) are used to illustrate the effectiveness of the proposed approach while considering only a geometric random field. Compared to Monte Carlo Simulation (MCS), the proposed random field approach is appeared to be very accurate and efficient. Moreover, the results show that the random field variation cannot be neglected for probability analysis and design practices.
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Daskalakis, Constantinos, Ilias Diakonikolas, Ryan ODonnell, Rocco A. Servedio, and Li-Yang Tan. "Learning Sums of Independent Integer Random Variables." In 2013 IEEE 54th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2013. http://dx.doi.org/10.1109/focs.2013.31.

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Karloff, Howard, and Yishay Mansour. "On construction of k-wise independent random variables." In the twenty-sixth annual ACM symposium. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/195058.195409.

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De, Anindya, Philip M. Long, and Rocco A. Servedio. "Learning Sums of Independent Random Variables with Sparse Collective Support." In 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 2018. http://dx.doi.org/10.1109/focs.2018.00036.

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Kuo, C. J., and Y. F. Hsu. "On the quantization efficiency of independent and uncorrelated random variables." In [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE, 1992. http://dx.doi.org/10.1109/icassp.1992.226349.

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Reports on the topic "Product of independent random variables"

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Niang, Aladji Babacar, Gane Samb Lo, and Moumouni Diallo. Asymptotic laws of summands I: square integrable independent random variables. Arxiv, August 2021. http://dx.doi.org/10.16929/hs/imhotep.2021.x.002.

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This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review exposition but specially as a complete exposition expect a few exterior resources. For graduate students and for researchers (beginners or advanced), any paper of the series should be considered as a basis for constructing new results. The contents are taken from advanced books but the organization and the proofs use more recent tools, are given in more details and do not systematically follow previous one. Sometimes, theorems are completed and innovated
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Schlenker, George J. Methods for Calculating the Probability Distribution of Sums of Independent Random Variables. Fort Belvoir, VA: Defense Technical Information Center, July 1986. http://dx.doi.org/10.21236/ada170465.

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Schulz, Jan, Daniel Mayerhoffer, and Anna Gebhard. A Network-Based Explanation of Perceived Inequality. Otto-Friedrich-Universität, 2021. http://dx.doi.org/10.20378/irb-49393.

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Across income groups and countries, the public perception of economic inequality and many other macroeconomic variables such as inflation or unemployment rates is spectacularly wrong. These misperceptions have far-reaching consequences, as it is perceived inequality, not actual inequality informing redistributive preferences. The prevalence of this phenomenon is independent of social class and welfare regime, which suggests the existence of a common mechanism behind public perceptions. We propose a network-based explanation of perceived inequality building on recent advances in random geometric graph theory. The literature has identified several stylised facts on how individual perceptions respond to actual inequality and how these biases vary systematically along the income distribution. Our generating mechanism can replicate all of them simultaneously. It also produces social networks that exhibit salient features of real-world networks; namely, they cannot be statistically distinguished from small-world networks, testifying to the robustness of our approach. Our results, therefore, suggest that homophilic segregation is a promising candidate to explain inequality perceptions with strong implications for theories of consumption behaviour.
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Nuttall, Albert H. Joint Probability Density Function of Selected Order Statistics and the Sum of the Remainder as Applied to Arbitrary Independent Random Variables. Fort Belvoir, VA: Defense Technical Information Center, November 2003. http://dx.doi.org/10.21236/ada419339.

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Edwards, Susan L., Marcus E. Berzofsky, and Paul P. Biemer. Addressing Nonresponse for Categorical Data Items Using Full Information Maximum Likelihood with Latent GOLD 5.0. RTI Press, September 2018. http://dx.doi.org/10.3768/rtipress.2018.mr.0038.1809.

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Full information maximum likelihood (FIML) is an important approach to compensating for nonresponse in data analysis. Unfortunately, only a few software packages implement FIML and even fewer have the capability to compensate for missing not at random (MNAR) nonresponse. One of these packages is Statistical Innovations’ Latent GOLD; however, the user documentation for Latent GOLD provides no mention of this capability. The purpose of this paper is to provide guidance for fitting MNAR FIML models for categorical data items using the Latent GOLD 5.0 software. By way of comparison, we also provide guidance on fitting FIML models for nonresponse missing at random (MAR) using the methods of Fuchs (1982) and Fay (1986), who incorporated item nonresponse indicators within a structural modeling framework. We compare both FIML for MAR and FIML for MNAR nonresponse models for independent and dependent variables. Also, we provide recommendations for future applications of FIML using Latent GOLD.
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