On computing distributions of products of non-negative independent random variables

Applied and Computational Harmonic Analysis - Tập 46 - Trang 400-416 - 2019
Gregory Beylkin1, Lucas Monzón1, Ignas Satkauskas1
1Department of Applied Mathematics, University of Colorado at Boulder, UCB 526, Boulder, CO 80309-0526, United States

Tài liệu tham khảo

Abramowitz, 1970 Adamjan, 1968, Infinite Hankel matrices and generalized Carathéodory–Fejér and I. Schur problems, Funktsional. Anal. i Prilozhen., 2, 1, 10.1007/BF01075356 Adamjan, 1968, Infinite Hankel matrices and generalized problems of Carathéodory–Fejér and F. Riesz, Funktsional. Anal. i Prilozhen., 2, 1, 10.1007/BF01075356 Adamjan, 1971, Analytic properties of the Schmidt pairs of a Hankel operator and the generalized Schur–Takagi problem, Math. USSR, Sb., 15, 34, 10.1070/SM1971v015n01ABEH001531 Andrews, 1999, Special Functions, vol. 71 Beylkin, 2005, On approximation of functions by exponential sums, Appl. Comput. Harmon. Anal., 19, 17, 10.1016/j.acha.2005.01.003 Beylkin, 2009, Nonlinear inversion of a band-limited Fourier transform, Appl. Comput. Harmon. Anal., 27, 351, 10.1016/j.acha.2009.04.003 Beylkin, 2010, Approximation of functions by exponential sums revisited, Appl. Comput. Harmon. Anal., 28, 131, 10.1016/j.acha.2009.08.011 Beylkin, 2017, On computing distributions of products of random variables via Gaussian multiresolution analysis, Appl. Comput. Harmon. Anal. Chen, 2012, Novel approximations to the statistics of products of independent random variables and their applications in wireless communications, IEEE Trans. Veh. Technol., 61, 443, 10.1109/TVT.2011.2178441 Cheng, 2005, On the compression of low-rank matrices, SIAM J. Sci. Comput., 205, 1389, 10.1137/030602678 NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/, Release 1.0.13 of 2016-09-16. F.W.J. Olver, A.B. Olde Daalhuis, D.W. Lozier, B.I. Schneider, R.F. Boisvert, C.W. Clark, B.R. Miller and B.V. Saunders (Eds.). Epstein, 1948, Some applications of the Mellin transform in statistics, Ann. Math. Stat., 19, 370, 10.1214/aoms/1177730201 Gradshteyn, 2015 Halko, 2011, Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions, SIAM Rev., 53, 217, 10.1137/090771806 Haut, 2012, Fast and accurate con-eigenvalue algorithm for optimal rational approximations, SIAM J. Matrix Anal. Appl., 33, 1101, 10.1137/110821901 Horn, 1990 Hua, 1988, Matrix pencil method and its performance, vol. 4, 2476 Hua, 1990, Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise, IEEE Trans. Acoust. Speech Signal Process., 38, 814, 10.1109/29.56027 Hua, 1991, On SVD for estimating generalized eigenvalues of singular matrix pencil in noise, IEEE Trans. Signal Process., 39, 892, 10.1109/78.80911 Kung, 1983, State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem, J. Opt. Soc. Amer., 73, 1799, 10.1364/JOSA.73.001799 Liberty, 2007, Randomized algorithms for the low-rank approximation of matrices, Proc. Natl. Acad. Sci. USA, 104, 20167, 10.1073/pnas.0709640104 Lomnicki, 1967, On the distribution of products of random variables, J. Roy. Statist. Soc. Ser. B, 29, 513 Nadarajah, 2006, On the product and ratio of Gamma and Weibull random variables, Econometric Theory, 22, 338, 10.1017/S0266466606060154 Reynolds, 2013, Rational approximations for tomographic reconstructions, Inverse Probl., 29, 10.1088/0266-5611/29/6/065020 Shakil, 2007, On the product of Maxwell and Rice random variables, J. Mod. Appl. Stat. Methods, 6, 212, 10.22237/jmasm/1177993080 Springer, 1979 Springer, 1966, The distribution of products of independent random variables, SIAM J. Appl. Math., 14, 511, 10.1137/0114046 Zheng, 2012, Approximation to distribution of product of random variables using orthogonal polynomials for lognormal density, IEEE Commun. Lett., 16, 2028, 10.1109/LCOMM.2012.101712.122141