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