Zobrazeno 1 - 10
of 610
pro vyhledávání: '"Gaunt, Robert"'
Autor:
Gaunt, Robert E., Ye, Zixin
We derive asymptotic expansions for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables. As a
Externí odkaz:
http://arxiv.org/abs/2411.03942
Autor:
Gaunt, Robert E.
Building on the rather large literature concerning the regularity of the solution of the standard normal Stein equation, we provide a complete description of the best possible uniform bounds for the derivatives of the solution of the standard normal
Externí odkaz:
http://arxiv.org/abs/2410.05475
Autor:
Gaunt, Robert E.
We represent the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, as a difference of two independent noncentral chi-square random variables (which we refer to as the noncent
Externí odkaz:
http://arxiv.org/abs/2408.04101
We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads to explic
Externí odkaz:
http://arxiv.org/abs/2407.02299
We prove that the distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of independent
Externí odkaz:
http://arxiv.org/abs/2405.10178
Autor:
Gaunt, Robert E.
We obtain exact formulas for the absolute raw and central moments of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. When the skewness p
Externí odkaz:
http://arxiv.org/abs/2404.13709
We 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 characterisa
Externí odkaz:
http://arxiv.org/abs/2402.02264
Autor:
Gaunt, Robert E., Li, Siqi
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including formulas for the
Externí odkaz:
http://arxiv.org/abs/2401.17446
We use Stein characterisations to derive new moment-type estimators for the parameters of several truncated multivariate distributions in the i.i.d. case; we also derive the asymptotic properties of these estimators. Our examples include the truncate
Externí odkaz:
http://arxiv.org/abs/2312.09344
A celebrated result in probability theory is that a simple symmetric random walk on the $d$-dimensional lattice $\mathbb{Z}^d$ is recurrent for $d=1,2$ and transient for $d\geq 3$. In this note, we derive a closed-form expression, in terms of the Lau
Externí odkaz:
http://arxiv.org/abs/2311.11326