Mixture Distributions

Create a mixture distribution, which can be thought of as an average of multiple distributions (in terms of their CDF, density, PMF, or survival functions, for example). Data drawn from a mixture distribution involves two steps: first randomly selecting the distribution to draw from, followed by the random selection from that distribution.

Usage

mix(
  ...,
  weights = 1,
  na_action_dst = c("null", "drop", "fail"),
  na_action_w = c("null", "drop", "fail")
)

Arguments

...

Distribution objects, or list of distributions.

weights

Vector of weights corresponding to the distributions; or, single numeric for equal weights. When normalized, they correspond to the probabilities of selecting each distribution.

na_action_dst, na_action_w

What should be done with null distributions in ... and NA in weights? Character vector of length 1: one of "fail", "null" (default), or "drop". See details.

Value

A mixture distribution.

Details

Distributions in ... and the weights vector are recycled to have the same length, but only if one of them has length 1 (via vctrs::vec_recycle_common()).

na_action_dst and na_action_w specify the NA action for distributions and weights. "NA" here means either NA in the weights vector, or a Null distribution (distionary::dst_null()) in the distributions. Options are, in order of precedence:

• "fail": Throw an error in the presence of NAs.

• "null": Return a Null distribution in the presence of NAs.

• "drop": Remove distribution-weight pairs having an NA value

Examples

library(distionary)
a <- dst_norm(0, 1)
b <- dst_norm(5, 2)
m1 <- mix(a, b, weights = c(1, 4))
plot(a, col = "red", lty = 2, from = -3, to = 11)
plot(b, add = TRUE, col = "blue", lty = 2)
plot(m1, add = TRUE)
legend(
  "topright",
   legend = c("Mixture", "N(0,1)", "N(5,2)"),
   col = c("black", "red", "blue"),
   lty = c(1, 2, 2)
)