Computes the log-likelihood for i.i.d. gamma observations.
L(α,β|x) = nαlog(β) - n*log(Γ(α)) + (α-1)Σlog(xᵢ) - βΣxᵢ
Usage
loglik_gamma(shape, rate, x)
Arguments
- shape
Shape parameter α (value object), must be positive
- rate
Rate parameter β (value object), must be positive
- x
Numeric vector of observations (must be positive)
Value
A value object representing the log-likelihood
Details
The gamma distribution is parameterized with shape α and rate β,
where EX = α/β and VarX = α/β².