The law of X when \(\theta \sim W\) and
\(X \sim P_\theta\). Both the alternative
\(Q = P_{W_1}\) and the fitted
\(\widehat{P}^* = P_{\widehat{W}_0}\) are of this form.
format() names the family and how it was mixed, distinguishing
a point mass from a genuine mixture.
Arguments
- family
The parametric_family whose kernel is pushed forward.
- mixing
A distribution over its parameter space, or a parameter vector for a point mass.
Details
A bare parameter vector is taken as a point mass. Calling the family,
fam(theta) or fam(W), is the usual shorthand.
Examples
fam <- multinomial_family(n_trials = 4L, k = 3L)
mixture(fam, c(0.5, 0.3, 0.2))
#> <mixture> multinomial_family at theta = (0.5, 0.3, 0.2)
mixture(fam, finite_dist(
atoms = rbind(c(0.6, 0.2, 0.2), c(0.2, 0.6, 0.2)),
weights = c(0.5, 0.5)
))
#> <mixture> multinomial_family mixed over 2 atoms