Results 1 to 10 of about 49,438 (77)
The basic distributional theory for the product of zero mean correlated normal random variables
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
openaire +6 more sources
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
openaire +6 more sources
Asymptotic approximations for the distribution of the product of correlated normal random variables
Journal of Mathematical Analysis and Applications20 ...
Robert E. Gaunt, Zixin Ye
openaire +5 more sources
A Stein characterisation of the distribution of the product of correlated normal random variables
Statistics & Probability LettersWe obtain a Stein characterisation of the distribution of the product of two correlated normal random variables with non-zero means, and more generally the distribution of the sum of independent copies of such random variables. Our Stein characterisation is shown to naturally generalise a number of other Stein characterisations in the literature.
Robert E. Gaunt +2 more
openaire +5 more sources
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
doaj +1 more source
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.
openaire +4 more sources
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 ...
openaire +2 more sources
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 ...
openaire +3 more sources