observ_ts {BLModel}

Example of distribution of views – Student t-distribution

Description

Function observ_ts computes density of Student t-distribution of views using the formula
f(x) = c_k*(1 +(x-q)^{T}*\Sigma^{-1}*(x-q)/df)^{(-(df+k)/2)},
where c_k is a normalization constant (depends on the dimension of x and q) and \Sigma is the dispersion matrix.

Usage

observ_ts(x, q, covmat, df = 5)

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.

df

Number of degrees of freedom of Students t-distribution.

Value

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

References

Kotz, S., Nadarajah, S., Multivariate t Distributions and Their Applications. Cambridge University Press, 2004.

Examples

k =3
observ_ts (x = matrix(c(rep(0.5,k),rep(0.2,k)),k,2), q = matrix(0,k,1), covmat = diag(k), 
         df=5)