observ_powerexp {BLModel}

Example of distribution of views – power exponential distribution

Description

Function observ_powerexp computes density of power exponential distribution of views using the formula
f(x) = c_k*\exp(- ((x-q)^{T}*\Sigma^{-1}*(x-q))^{\beta}/2),
where c_k is a normalization constant (depends on the dimension of x and q) and \Sigma is the dispersion matrix.

Usage

observ_powerexp(x, q, covmat, beta = 0.6)

Arguments

x

Data points matrix which collects in rows coordinates of points in which distribution density is computed.

q

Vector of investor's views.

covmat

Covariance matrix of the distribution; dispersion matrix \Sigma is computed from covmat.

beta

Shape parameter of the power exponential distribution.

Value

function returns a vector of distribution densities in data points x.

References

Gomez, E., Gomez-Villegas, M., Marin, J., A multivariate generalization of the power exponential family of distributions. Commun. Statist. Theory Methods, 27 (1998), 589–600. DOI: 10.1080/03610929808832115

Examples

k =3
observ_powerexp (x = matrix(c(rep(0.5,k),rep(0.2,k)),k,2), q = matrix(0,k,1),
               covmat = diag(k), beta = 0.6)