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Trim (condition) a distribution

Source: R/verb-trim.R
trim.Rd

Discard the probability lying to one side of a value, and scale up what remains so that it sums to 1 again. trim_left() discards the probability below of, giving the distribution of the variable conditioned on landing at or above it; trim_right() discards the probability above of, conditioning on landing at or below.

Usage

trim_left(distribution, of, ..., knot = c("keep", "discard", "split"))

trim_right(distribution, of, ..., knot = c("keep", "discard", "split"))

Arguments

distribution

Distribution to trim.

of

Value on the real line defining where to trim (single numeric).

...

Currently unused; must be empty.

knot

What to do with the probability sitting exactly on of: "keep" it (the default), "discard" it with the trimmed side, or "split" it evenly between the two sides. Only has an effect where of carries probability. See Details.

Value

The conditional distribution, renormalised to total probability 1; or the Null distribution, if the trim leaves nothing behind.

What knot does

of is the knot: the point the trim cuts at. knot says what becomes of the probability sitting exactly on it, and matters only when the knot carries mass of its own, as an atom does. Where there is no mass exactly at of — anywhere in a continuous distribution — all three actions give the same answer.

  • "keep" (default) retains it, so trim_left(d, of) keeps outcomes greater than or equal to of. The knot is not on the side being trimmed away: of is not to the left of itself.

  • "discard" throws the knot away with that side, so trim_left(d, of) keeps outcomes strictly greater than of. Under this setting the probability kept is exactly distionary::prob_right(d, of, inclusive = FALSE), and a left and a right trim at the same knot share nothing.

  • "split" retains half of it. This is the mid-p convention used in discrete inference, where a boundary atom is shared evenly between the two sides rather than assigned wholly to one.

Whatever is retained is renormalised along with the rest, so the result is always a distribution in its own right.

Values of of with nothing beside them

If of falls in a gap in the support, the trim takes effect where the support resumes. Trimming a distribution living on [1, 2] and [4, 5] to the left of 3 gives one living on [4, 5].

If the trim leaves no probability at all — trimming a Uniform(0, 1) to the left of 2, say — the result is the Null distribution, distionary::dst_null().

See also

graft_left() and graft_right(), which replace a tail rather than discarding it.

Examples

d <- distionary::dst_norm(0, 1)
d <- trim_left(d, -2)
d <- trim_right(d, 2)
distionary::enframe_cdf(d, at = -3:3)
#> # A tibble: 7 × 2
#>    .arg   cdf
#>   <int> <dbl>
#> 1    -3 0    
#> 2    -2 0    
#> 3    -1 0.142
#> 4     0 0.5  
#> 5     1 0.858
#> 6     2 1    
#> 7     3 1    

# A Poisson has an atom at 5, so the knot is visible there. By default
# the trim keeps it.
d <- distionary::dst_pois(3)
distionary::eval_pmf(trim_left(d, 5), at = 5)
#> Loading required namespace: testthat
#> [1] 0.5457431
distionary::eval_pmf(trim_left(d, 5, knot = "discard"), at = 5)
#> [1] 0
distionary::eval_pmf(trim_left(d, 5, knot = "split"), at = 5)
#> [1] 0.3752728