Stein’s method and the distribution of the product of zero mean correlated normal random variables [PDF]
Communications in Statistics - Theory and Methods, 2019 Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a recent technique from the Stein's method literature to obtain a simple new proof, which also serves as an exposition ...
Robert E. Gaunt
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The basic distributional theory for the product of zero mean correlated normal random variables [PDF]
Statistica Neerlandica, 2022 AbstractThe product of two zero mean correlated normal random variables, and more generally the sum of independent copies of such random variables, has received much attention in the statistics literature and appears in many application areas. However, many important distributional properties are yet to be recorded.
Robert E. Gaunt
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On the distribution of the product of correlated normal random variables
Comptes Rendus. Mathématique, 2015 We solve a problem that has remained unsolved since 1936 – the exact distribution of the product of two correlated normal random variables. As a by-product, we derive the exact distribution of the mean of the product of correlated normal random variables.
Nadarajah, Saralees, Pogány, Tibor K.
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A note on the distribution of the product of zero‐mean correlated normal random variables [PDF]
Statistica Neerlandica, 2018 The problem of finding an explicit formula for the probability density function of two zero‐mean correlated normal random variables dates back to 1936. Perhaps, surprisingly, this problem was not resolved until 2016. This is all the more surprising given that a very simple proof is available, which is the subject of this note; we identify the product ...
Robert E. Gaunt
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Asymptotic Expansions Relating to the Distribution of the Product of Correlated Normal Random Variables [PDF]
Studies in Applied MathematicsABSTRACTAsymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with nonzero means and arbitrary variances, and more generally the sum of independent copies of such random variables. Asymptotic approximations are also given for the quantile function.
Robert E. Gaunt, Zixin Ye
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Asymptotic approximations for the distribution of the product of correlated normal random variables [PDF]
Journal of Mathematical Analysis and Applications, 2023 20 ...
Robert E. Gaunt, Zixin Ye
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Infinite divisibility of the product of two correlated normal random variables and exact distribution of the sample mean [PDF]
Journal of Mathematical Analysis and Applications15 ...
Robert E. Gaunt +2 more
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The variance-gamma ratio distribution
Comptes Rendus. Mathématique, 2023 Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived.
Gaunt, Robert E., Li, Siqi
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Note on the moment generating function of the multivariate normal distribution
Miskolc Mathematical NotesWe present a streamlined proof of a formula for the derivatives of the moment generating function of the multivariate normal distribution. We formulate it in terms of the summation of the contractions by pairings, which encodes a combinatorial ...
Kenichi Hirose
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Note on uncertainty in Monte Carlo dose calculations and its relation to microdosimetry
Zeitschrift für Medizinische PhysikPurpose: The Type A standard uncertainty in Monte Carlo (MC) dose calculations is usually determined using the “history by history” method. Its applicability is based on the assumption that the central limit theorem (CLT) can be applied such that the ...
Günther H. Hartmann, Hans G. Menzel
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