Laplace exponent of a gamma completely random measure

Returns \(a \log(1 + f)\), the Laplace exponent of a gamma process with unit rate evaluated at the test function value f; the Laplace transform itself is \(\exp(-a \log(1 + f))\).

Usage

morie_gh_crm_laplace_gamma(f, a)

Arguments

f

non-negative test-function value (or vector of values)

a

base-measure mass of the gamma completely random measure

Value

numeric vector of Laplace exponents, matching the length of f

References

Ghosal, S. and van der Vaart, A. (2017). Fundamentals of Nonparametric Bayesian Inference. Cambridge University Press.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_gh_crm_laplace_gamma(V, V)
#> [1]  0.6931472  2.1972246  4.1588831  6.4377516  8.9587973 11.6754609 14.5560908
#> [8] 17.5777966