observ_powerexp: Example of distribution of views - power exponential...

In BLModel: Black-Litterman Posterior Distribution

Description

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

BLModel documentation built on May 2, 2019, 5:11 a.m.