distplyr (version 0.2.0)

maximize: Extremum of Several Distributions

Description

For a collection of distributions, obtain the distributions of the maximum (maximize()) and minimum (minimize()) from independent draws of each component distribution.

Aliases maximise() and minimise() are also provided.

Usage

maximize(
  ...,
  draws = 1,
  na_action_dst = c("null", "drop", "fail"),
  na_action_draws = c("null", "drop", "fail")
)
minimize(
  ...,
  draws = 1,
  na_action_dst = c("null", "drop", "fail"),
  na_action_draws = c("null", "drop", "fail")
)

Value

A distribution corresponding to the maximum or minimum.

Arguments

...

Distribution objects, or list of distributions.

draws

Number of draws from each distribution considered in the maximum (possibly not integer, but never negative). Either a single numeric applying to all distributions in ..., or a vector matching the number of distributions in ....

na_action_dst, na_action_draws

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

Details

To give an example of what distribution is returned, if X1 and X2 are two random variables with distributions D1 and D2 respectively, then maximize(D1, D2, draws = c(2, 3)) returns the distribution of max(X1, X1, X2, X2, X2).

Distributions in ... and the draws 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_draws specify the NA action for distributions and draws. "NA" here means either NA in the draws 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

Simplifications made in these functions include the following:

• If any distributions are entirely to the left (right) of others, then they are removed from consideration in maximize() (minimize()).

• If all Finite distributions are input, the result is also a Finite distribution.

• If the same distribution is input multiple times, their corresponding draws are summed.

Examples

library(distionary)
# One is always more extreme than the other in this case.
d1 <- dst_unif(-1, 2)
d2 <- dst_unif(5, 6)
maximize(d1, d2) # d2
minimize(d1, d2) # d1

# Visualizing the maximum and minimum
d3 <- dst_norm(4, 1)
d4 <- dst_exp(0.3)

dmax <- maximize(d3, d4, draws = 1:2)
dmin <- minimize(d3, d4, draws = 1:2)

# Maximum
plot(d3, col = "blue", lty = 2, from = 0, to = 14)
plot(d4, col = "red", lty = 2, add = TRUE)
plot(dmax, add = TRUE, n = 1000)
legend(
 "topright",
 legend = c("Maximum", "N(4,1)", "Exp(0.3)"),
 col = c("black", "blue", "red"),
 lty = c(1, 2, 2)
)

# Minimum
plot(d3, col = "blue", lty = 2, from = 0, to = 10)
plot(d4, col = "red", lty = 2, add = TRUE)
plot(dmin, add = TRUE, n = 1000)
legend(
  "topright",
  legend = c("Minimum", "N(4,1)", "Exp(0.3)"),
  col = c("black", "blue", "red"),
  lty = c(1, 2, 2)
)