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Multivariate gamma random field from a shared component

Source: R/schab_book_methods.R
mgamrf.Rd

Schabenberger & Gotway (2005) Problem 2.3: Z(s_i) = X_0 + X_i with independent X_i ~ Gamma(alpha_i, beta) (mean alpha_i beta). Then Cov(Z(s_i), Z(s_j)) = alpha_0 beta^2 for i != j, Var(Z(s_i)) = (alpha_0 + alpha_i) beta^2, Z(s_i) ~ Gamma(alpha_0 + alpha_i, beta), and the field is second-order stationary exactly when alpha_1 = ... = alpha_n.

Usage

mgamrf(alpha, beta)

Arguments

alpha

Shapes (alpha_0, alpha_1, ..., alpha_n), positive.

beta

Common scale, positive.

Value

Named list: mean, cov, corr, shape, scale, stationary.

References

Schabenberger & Gotway (2005), Problem 2.3, p. 79.

Examples

mgamrf(c(2, 1, 1, 3), 0.5)$corr
#>           [,1]      [,2]      [,3]
#> [1,] 1.0000000 0.6666667 0.5163978
#> [2,] 0.6666667 1.0000000 0.5163978
#> [3,] 0.5163978 0.5163978 1.0000000