Gaussian statistics for palaeomagnetic vectors

Gaussian statistics for palaeomagnetic vectors

S U M M A R Y With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spher...

Autoregressive Gaussian Random Vectors of First Order

Balancing Gaussian Vectors

Let x1, . . . xn be independent normally distributed vectors on Rd. We determine the distribution function of the minimum norm of the 2n vectors ±x1 ± x2 · · · ± xn.

Gaussian Random Vectors

1. The multivariate normal distribution Let X := (X1 � � � � �X�) be a random vector. We say that X is a Gaussian random vector if we can write X = μ + AZ� where μ ∈ R, A is an � × � matrix and Z := (Z1 � � � � �Z�) is a �-vector of i.i.d. standard normal random variables. Proposition 1. Let X be a Gaussian random vector, as above. Then, EX = μ� Var(X) := Σ = AA� and MX(�) = e � μ+ 1 2 �A���2 =...

autoregressive gaussian random vectors of first order