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Relevant bibliographies by topics / Approximating a function of random variables

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Academic literature on the topic 'Approximating a function of random variables'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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Journal articles on the topic "Approximating a function of random variables"

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Wille, Emilio. "APPROXIMATING PROBABILITY DISTRIBUTION FUNCTIONS WITH FEW MOMENTS." Latin American Applied Research - An international journal 50, no. 1 (2019): 21–25. http://dx.doi.org/10.52292/j.laar.2020.132.

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A procedure is presented for approximating a given probability distribution function or statistical data considering a subset of their moments.This is done by a method of fitting moments of a piecewise linear functionto the moments of the known data. The approach has many advantages over popular approximation approaches. The procedure is demonstrated with commonly used cdfs (Exponential, Gamma, Log-Normal, Normal) andmore difficult problems involving sum and product of random variables,obtaining good agreement between the theoretical/simulation curves and the piecewise linear approximations.

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Ding, Guoli, Robert F. Lax, Peter Chen, and Jianhua Chen. "Asymptotic Behavior of Linear Approximations of Pseudo-Boolean Functions." Journal of Advanced Computational Intelligence and Intelligent Informatics 11, no. 4 (2007): 403–9. http://dx.doi.org/10.20965/jaciii.2007.p0403.

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We study the problem of approximating pseudo-Boolean functions by linear pseudo-Boolean functions. Pseudo-Boolean functions generalize ordinary Boolean functions by allowing the function values to be real numbers instead of just the 0-1 values. Pseudo-Boolean functions have been used by AI and theorem proving researchers for efficient constraint satisfaction solving. They can also be applied for modeling uncertainty. We investigate the possibility of efficiently computing a linear approximation of a pseudo-Boolean function of arbitrary degree. We show some example cases in which a simple (effi

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Pommeret, Denys, and Laurence Reboul. "Approximating the Probability Density Function of a Transformation of Random Variables." Methodology and Computing in Applied Probability 21, no. 2 (2018): 633–45. http://dx.doi.org/10.1007/s11009-018-9629-0.

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Seijas-Macías, Antonio, Amílcar Oliveira, Teresa A. Oliveira, and Víctor Leiva. "Approximating the Distribution of the Product of Two Normally Distributed Random Variables." Symmetry 12, no. 8 (2020): 1201. http://dx.doi.org/10.3390/sym12081201.

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The distribution of the product of two normally distributed random variables has been an open problem from the early years in the XXth century. First approaches tried to determinate the mathematical and statistical properties of the distribution of such a product using different types of functions. Recently, an improvement in computational techniques has performed new approaches for calculating related integrals by using numerical integration. Another approach is to adopt any other distribution to approximate the probability density function of this product. The skew-normal distribution is a g

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Khuri, A. I., S. Mukhopadhyay, and M. A. Khuri. "Approximating moments of continuous functions of random variables using Bernstein polynomials." Statistical Methodology 24 (May 2015): 37–51. http://dx.doi.org/10.1016/j.stamet.2014.11.004.

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Gertner, George Z. "The sensitivity of measurement error in stand volume estimation." Canadian Journal of Forest Research 20, no. 6 (1990): 800–804. http://dx.doi.org/10.1139/x90-105.

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A method is given for approximating and evaluating the consequences of random and nonrandom errors in the independent variables of a nonlinear tree volume function that is used in the estimation of stand volume based on a simple random sample of plots. Sampling error, regression function error, and measurement error are accounted for with the method presented. An application is given where relatively moderate amounts of measurement error in the independent variables of a tree volume function can cause a relatively large reduction in the accuracy of estimated stand volume.

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Gutman, I., та M. Rašković. "Monte Carlo Approach to Total π-Electron Energy of Conjugated Hydrocarbons". Zeitschrift für Naturforschung A 40, № 10 (1985): 1059–61. http://dx.doi.org/10.1515/zna-1985-1013.

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Approximating the π-electron molecular orbital energy levels by uniformly distributed random variables, a McClelland-type formula for the total π-electron energy is obtained. Conditions are determined under which a given distribution function will result in a formula of McClelland type.

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WAGNER, ROY. "Tail Estimates for Sums of Variables Sampled by a Random Walk." Combinatorics, Probability and Computing 17, no. 2 (2008): 307–16. http://dx.doi.org/10.1017/s0963548307008772.

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We prove tail estimates for variables of the form ∑if(Xi), where (Xi)i is a sequence of states drawn from a reversible Markov chain, or, equivalently, from a random walk on an undirected graph. The estimates are in terms of the range of the function f, its variance, and the spectrum of the graph. The purpose of our estimates is to determine the number of chain/walk samples which are required for approximating the expectation of a distribution on vertices of a graph, especially an expander. The estimates must therefore provide information for fixed number of samples (as in Gillman's [4]) rather

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Zhao, Wei Tao, Yi Yang, and Tian Jun Yu. "Reliability-Based Structural Optimization Using Sequential Response Surface Method." Advanced Materials Research 532-533 (June 2012): 1503–6. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.1503.

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A design method of reliability-based structural optimization has a powerful advantage because some random variables can be considered. However, the sensitivity analysis of reliability with respect to random variables is very complicated and its computational cost is very expensive. Thus, a response surface method is adopted for approximating the limit state function to improve computational efficiency. An iterative strategy is used to determine a response surface that is able to fit the limit state function in the neighborhood of the design point. A sequential response surface method is perfor

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Kovalenko, I. N., A. N. Nakonechnyi, and A. B. Romanov. "Chebyshev approximation of the distribution function of nonnegative random variables." Cybernetics and Systems Analysis 32, no. 2 (1996): 211–18. http://dx.doi.org/10.1007/bf02366534.

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Dissertations / Theses on the topic "Approximating a function of random variables"

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Eriksson, Anders. "Essays on Gaussian Probability Laws with Stochastic Means and Variances : With Applications to Financial Economics." Doctoral thesis, Uppsala University, Department of Information Science, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5777.

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<p>This work consists of four articles concerning Gaussian probability laws with stochastic means and variances. The first paper introduces a new way of approximating the probability distribution of a function of random variables. This is done with a Gaussian probability law with stochastic mean and variance. In the second paper an extension of the Generalized Hyperbolic class of probability distributions is presented. The third paper introduces, using a Gaussian probability law with stochastic mean and variance, a GARCH type stochastic process with skewed innovations. </p><p>In the fourth pap

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GURUMURTHY, ARAVIND. "A GENETIC ALGORITHM TECHNIQUE FOR APPROXIMATING FUNCTIONS OF MULTIPLE INDEPENDENT VARIABLES." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1065654138.

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Kharoufeh, Jeffrey P. "Density estimation for functions of correlated random variables." Ohio : Ohio University, 1997. http://www.ohiolink.edu/etd/view.cgi?ohiou1177097417.

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Lee, Jin Woo. "Multi-level Decoupled Optimization of Wind Turbine Structures Using Coefficients of Approximating Functions as Design Variables." University of Toledo / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1501003238831086.

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Gaunt, Robert E. "Rates of convergence of variance-gamma approximations via Stein's method." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:5ddc6def-5821-4e72-8784-cfe2dc8b6c03.

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Stein's method is a powerful technique that can be used to obtain bounds for approximation errors in a weak convergence setting. The method has been used to obtain approximation results for a number of distributions, such as the normal, Poisson and Gamma distributions. A major strength of the method is that it is often relatively straightforward to apply it to problems involving dependent random variables. In this thesis, we consider the adaptation of Stein's method to the class of Variance-Gamma distributions. We obtain a Stein equation for the Variance-Gamma distributions. Uniform bounds for

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Pfister, Mark. "Distribution of a Sum of Random Variables when the Sample Size is a Poisson Distribution." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3459.

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A probability distribution is a statistical function that describes the probability of possible outcomes in an experiment or occurrence. There are many different probability distributions that give the probability of an event happening, given some sample size n. An important question in statistics is to determine the distribution of the sum of independent random variables when the sample size n is fixed. For example, it is known that the sum of n independent Bernoulli random variables with success probability p is a Binomial distribution with parameters n and p: However, this is not true when

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Pranskūnaitė, Arūnė. "Imčių iš baigtinių visumų statistikos tikimybiniai skirstiniai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20120620_114328-60725.

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Nagrinėjama silpnai priklausomų atsitiktinių dydžių statistika. Šio magistrinio darbo tikslas, turimą sumą, suvesti į nepriklausomų atsitiktinių dydžių sumą, kuri leistų tolimesniam tyrimui, pritaikyti žinomas teoremas, skaičiavimus bei rezultatus iš nepriklausomų atsitiktinių dydžių teorijos.<br>We analyze of weakly dependent random variables statistics. The objective of this master thesis is to deduce sum to independent random variables sum, which will be useful for applaying known theorems, calculations and results from the theory in independent random variables.

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ROCHA, Samy Marques. "Distribuição Binomial e Aplicações." Universidade Federal do Maranhão, 2017. http://tedebc.ufma.br:8080/jspui/handle/tede/1271.

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Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-04-07T15:18:02Z No. of bitstreams: 1 Samy marques.pdf: 1541887 bytes, checksum: 6335e5c12fc4f4fec24616c00e7613b4 (MD5)<br>Made available in DSpace on 2017-04-07T15:18:02Z (GMT). No. of bitstreams: 1 Samy marques.pdf: 1541887 bytes, checksum: 6335e5c12fc4f4fec24616c00e7613b4 (MD5) Previous issue date: 2017-02-16<br>The Binomial probability distribution is one of the most commonly used to represent data of discrete random variables. In this work, we present the construction of the Binomial model and its main characteristics. The relation

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Reding, Lucas. "Contributions au théorème central limite et à l'estimation non paramétrique pour les champs de variables aléatoires dépendantes." Thesis, Normandie, 2020. http://www.theses.fr/2020NORMR049.

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La thèse suivante traite du Théorème Central Limite pour des champs de variables aléatoires dépendantes et de son application à l’estimation non-paramétrique. Dans une première partie, nous établissons des théorèmes centraux limite quenched pour des champs satisfaisant une condition projective à la Hannan (1973). Les versions fonctionnelles de ces théorèmes sont également considérées. Dans une seconde partie, nous établissons la normalité asymptotique d’estimateurs à noyau de la densité et de la régression pour des champs fortement mélangeants au sens de Rosenblatt (1956) ou bien des champs fa

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Deltuvienė, Dovilė. "Asimptotiniai skleidiniai didžiųjų nuokrypių zonose." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2004~D_20050111_161823-34609.

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The novelty and originality of the work consists in the fact that in order to obtain asymptotic expansions with optimal values of the remainder terms in the zone of large deviations, along with the cumulant method the classical method of characteristic functions has to be used. In addition, when solving the problems stated in the work, other than the well known results in the problems of limit theorems of the probability theory and mathematical statistics, we have to estimate constants. Technically it is frequently rather a complicated task. The results obtained in the work have good opportuni

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Books on the topic "Approximating a function of random variables"

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Saff, E. B., Douglas Patten Hardin, Brian Z. Simanek, and D. S. Lubinsky. Modern trends in constructive function theory: Conference in honor of Ed Saff's 70th birthday : constructive functions 2014, May 26-30, 2014, Vanderbilt University, Nashville, Tennessee. American Mathematical Society, 2016.

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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-. American Mathematical Society, 2016.

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Merlevède, Florence, Magda Peligrad, and Sergey Utev. Functional Gaussian Approximation for Dependent Structures. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198826941.001.0001.

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This book has its origin in the need for developing and analyzing mathematical models for phenomena that evolve in time and influence each another, and aims at a better understanding of the structure and asymptotic behavior of stochastic processes. This monograph has double scope. First, to present tools for dealing with dependent structures directed toward obtaining normal approximations. Second, to apply the normal approximations presented in the book to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including

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Functional Gaussian Approximation For Dependent Structures. Oxford University Press, 2019.

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Hanfelt, John. General Estimating Function Theory. Chapman & Hall/CRC, 2009.

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V, Prokhorov I͡U︡, ed. Probability theory, function theory, mechanics. American Mathematical Society, 1990.

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Bohr-Jessen Limit Theorem, Revisited. Mathematical Society of Japan, 2014.

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United States. National Aeronautics and Space Administration., ed. Study of one- and two-dimensional filtering and deconvolution algorithms for a streaming array computer: Final report, appendix 5. National Aeronautics and Space Administration, 1985.

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Study of one- and two-dimensional filtering and deconvolution algorithms for a streaming array computer: Final report : [appendices]. National Aeronautics and Space Administration, 1985.

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United States. National Aeronautics and Space Administration., ed. Study of one- and two-dimensional filtering and deconvolution algorithms for a streaming array computer: Final report. National Aeronautics and Space Administration, 1985.

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Book chapters on the topic "Approximating a function of random variables"

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Walrand, Jean. "Multiplexing: B." In Probability in Electrical Engineering and Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-49995-2_4.

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AbstractChapter 10.1007/978-3-030-49995-2_3 used the Central Limit Theorem to determine the number of users that can safely share a common cable or link. We saw that this result is also fundamental to calculate confidence intervals. In this section, we prove this theorem. A key tool is the characteristic function that provides a simple way to study sums of independent random variables.Section 4.1 introduces the characteristic function and calculates it for a Gaussian random variable. Section 4.2 uses that function to prove the Central Limit Theorem. Section 4.3 uses the characteristic function to calculate the moments of a Gaussian random variable. The sum of squares of Gaussian random variables is a common model of noise in communication links. Section 4.4 proves a remarkable property of such a sum. Section 4.5 shows how to use characteristic functions to approximate binomial and geometric random variables. The error function arises in the calculation of the probability of errors in transmission systems and also in decisions based on random observations. Section 4.6 derives useful approximations of that function. Section 4.7 concludes the chapter with a discussion of an adaptive multiple access protocol similar to one used in WiFi networks.

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Bosq, Denis. "Sequences of Random Variables in Banach Spaces." In Linear Processes in Function Spaces. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1154-9_3.

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Astashkin, Sergey V. "The Comparison of Systems of Random Variables." In The Rademacher System in Function Spaces. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47890-2_7.

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Bosq, Denis. "Stochastic Processes and Random Variables in Function Spaces." In Linear Processes in Function Spaces. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1154-9_2.

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Ron, Dana, and Gilad Tsur. "On Approximating the Number of Relevant Variables in a Function." In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22935-0_57.

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Malyutov, M., and I. Tsitovich. "On sequential search for significant variables of unknown function." In Multidimensional Statistical Analysis and Theory of Random Matrices, edited by A. K. Gupta and V. L. Girko. De Gruyter, 1996. http://dx.doi.org/10.1515/9783110916690-014.

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Aouiti, Chaouki, Adel M. Alimi, and Aref Maalej. "A Genetic Designed Beta Basis Function Neural Network for Approximating Multi-Variables Functions." In Artificial Neural Nets and Genetic Algorithms. Springer Vienna, 2001. http://dx.doi.org/10.1007/978-3-7091-6230-9_95.

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Hoeffding, Wassily. "The Extrema of the Expected Value of a Function of Independent Random Variables." In Springer Series in Statistics. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0865-5_18.

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Hoeffding, Wassily, and S. S. Shrikhande. "Bounds for the Distribution Function of a Sum of Independent, Identically Distributed Random Variables." In Springer Series in Statistics. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-0865-5_16.

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Roussas, George G., and Debasis Bhattacharya. "Asymptotic Behavior of the Log-Likelihood Function in Stochastic Processes when Based on a Random Number of Random Variables." In Semi-Markov Models and Applications. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4613-3288-6_7.

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Conference papers on the topic "Approximating a function of random variables"

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Venkataraman, P. "Data Handling With Two Independent Variables and the Bezier Filter." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86330.

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Bezier functions of two independent variables are excellent vehicles for three dimensional data reduction that require preservation of derivative content. They can be applied to both smooth and noisy data. They represent the original data with good fidelity. The approximation is smooth and continuous to a high degree. The coefficients of the approximating Bezier function are obtained through a non iterative algebraic relation. These coefficients can replace the original data leading to significant data reduction. The Bezier function also allows the data over the entire domain to be represented

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Lin, Yao, Kiran Krishnapur, Janet K. Allen, and Farrokh Mistree. "Robust Design: Goal Formulations and a Comparison of Metamodeling Methods." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/dac-8608.

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Abstract In this paper, through theoretical analysis, we point out the limitations of goal formulations in previous methods for approximation-based robust design. Based on different philosophies and mathematical deduction, we propose three new methods to formulate robust design goals. Using a single variable function, we compare and contrast the use of response surface models and kriging models for approximating non-random, deterministic computer analyses in robust design with large variances of design variables in a highly nonlinear design space. Our preliminary conclusions are: 1) kriging mo

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Hu, Zhangli, and Xiaoping Du. "A Mean Value Reliability Method for Bimodal Distributions." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67279.

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In traditional reliability problems, the distribution of a basic random variable is usually unimodal; in other words, the probability density of the basic random variable has only one peak. In real applications, some basic random variables may follow bimodal distributions with two peaks in their probability density. For example, the random load of a bridge may have two peaks, with a distribution consisting of a weighted sum of two normal distributions, suggested by traffic load data. When binomial variables are involved, traditional reliability methods, such as the First Order Second Moment (F

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Leira, Bernt J. "A Comparison of Some Multivariate Weibull Distributions." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20678.

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Three different possible choices of statistical models for multivariate Weibull distributions are considered and compared. The concept of “a correlation field” is introduced and is subsequently applied for the purpose of comparing the different models. Linear combinations of Weibull distributed random variables are considered, and expressions for the corresponding probability density functions are established. Furthermore, a simplified procedure for approximating the resulting density function is described. Comparison is made between the statistical moments of increasing order for the specific

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Papadimitriou, Dimitrios I., Zissimos P. Mourelatos, and Zhen Hu. "Reliability Analysis Using Second-Order Saddlepoint Approximation and Mixture Distributions." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85267.

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This paper proposes a new second-order Saddlepoint Approximation (SOSA) method for reliability analysis of nonlinear systems with correlated non-Gaussian and multimodal random variables. The proposed method overcomes the limitation of current available SOSA methods which are applicable to problems with only Gaussian random variables, by employing a Gaussian Mixture Model (GMM). The latter is first constructed using the Expectation Maximization (EM) method to approximate the joint probability density function of the input variables. Expressions of the statistical moments of the response variabl

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Lee, Ikjin, Kyung K. Choi, Yoojeong Noh, Liang Zhao, and David Gorsich. "Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems With Correlated Random Variables." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28591.

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This study presents a methodology for computing stochastic sensitivities with respect to the design variables, which are the mean values of the input correlated random variables. Assuming that an accurate surrogate model is available, the proposed method calculates the component reliability, system reliability, or statistical moments and their sensitivities by applying Monte Carlo simulation (MCS) to the accurate surrogate model. Since the surrogate model is used, the computational cost for the stochastic sensitivity analysis is negligible. The copula is used to model the joint distribution of

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Yoo, David, and Ikjin Lee. "Sampling-Based Approach for Design Optimization in the Presence of Interval Variables." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13151.

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This paper proposes a methodology for sampling-based design optimization in the presence of interval variables. Assuming that an accurate surrogate model is available, the proposed method first searches the worst combination of interval variables for constraints when only interval variables are present or for probabilistic constraints when both interval and random variables are present. Due to the fact that the worst combination of interval variables for probability of failure does not always coincide with that for a performance function, the proposed method directly uses the probability of fa

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Du, Xiaoping. "Reliability-Based Design Using Saddlepoint Approximation." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99077.

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Reliability-based design optimization is much more computationally expensive than deterministic design optimization. To alleviate the computational demand, the First Order Reliability Method (FORM) is usually used in reliability-based design. Since FORM requires a nonlinear transformation from non-normal random variables to normal random variables, the nonlinearity of a constraint function may increase. As a result, the transformation may lead to a large error in reliability calculation. In order to improve accuracy, a new reliability-based design method with Saddlepoint Approximation is propo

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Papadimitriou, Dimitrios, and Zissimos P. Mourelatos. "Reliability-Based Topology Optimization Using Mean-Value Second-Order Saddlepoint Approximation." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67312.

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A reliability-based topology optimization (RBTO) approach is presented using a new mean-value second-order saddlepoint approximation (MVSOSA) method to calculate the probability of failure. The topology optimizer is based on a discrete adjoint formulation. MVSOSA is based on a second-order Taylor expansion of the limit state function at the mean values of the random variables. The first and second-order sensitivity derivatives of the limit state cumulant generating function with respect to the random variables in MVSOSA, are computed using direct-differentiation of the structural equations. Th

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Meng, Debiao, Hong-Zhong Huang, Huanwei Xu, Xiaoling Zhang, and Yan-Feng Li. "Sequential Multidisciplinary Design Optimization and Reliability Analysis Using an Efficient Third-Moment Saddlepoint Approximation Method." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46664.

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In Reliability based Multidisciplinary Design and Optimization (RBMDO), saddlepoint approximation has been utilized to improve reliability evaluation accuracy while sustaining high efficiency. However, it requires that not only involved random variables should be tractable; but also a saddlepoint can be obtained easily by solving the so-called saddlepoint equation. In practical engineering, a random variable may be intractable; or it is difficult to solve a highly nonlinear saddlepoint equation with complicated Cumulant Generating Function (CGF). To deal with these challenges, an efficient RBM

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Reports on the topic "Approximating a function of random variables"

1

Nuttal, Albert H. Saddlepoint Approximation and First-Order Correction Term to the Joint Probability Density Function of M Quadratic and Linear Forms in K Gaussian Random Variables With Arbitrary Means and Covariances. Defense Technical Information Center, 2000. http://dx.doi.org/10.21236/ada389100.

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2

Nuttall, Albert H. Joint Probability Density Function of Selected Order Statistics and the Sum of the Remaining Random Variables. Defense Technical Information Center, 2002. http://dx.doi.org/10.21236/ada399298.

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3

Nuttall, Albert H. Joint Probability Density Function of Selected Order Statistics and the Sum of the Remainder as Applied to Arbitrary Independent Random Variables. Defense Technical Information Center, 2003. http://dx.doi.org/10.21236/ada419339.

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