Gamma-conjugate posterior for an exponential or Poisson rate

Exponential data: shape k0 + n, rate lambda0 + sum(x); Poisson counts: shape k0 + sum(x), rate lambda0 + n (Hedderich, Sachs & Reynarowych 2023, Overview 30, whose Poisson row prints lambda0 x).

Usage

gmconj(
  x,
  k0,
  lambda0,
  likelihood = c("exponential", "poisson"),
  cred_level = 0.95
)

Arguments

x

Waiting times or counts.

k0, lambda0

Prior shape and rate.

likelihood

"exponential" or "poisson".

cred_level

Level of the equal-tailed credible interval.

Value

Named list: shape, rate, mean, lower, upper.

References

Gelman, A. et al. (2013). Bayesian Data Analysis, Sec. 2.6.

Examples

gmconj(c(0.8, 1.9, 0.4, 2.7, 1.1), 2, 1)$mean
#> [1] 0.8860759