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Score difference bounds -> sub-Gaussian / sub-exponential scale

Source: R/utils.R
score_diff_scales.Rd

Given score-difference bounds [lo, hi], computes the two scale constants used elsewhere in seqcomp:

  • c_thm1 = (hi - lo) / 2 — sub-Gaussian scale for Theorem 1, where |delta_i| <= c_thm1.

  • c_thm23 = hi - lo — sub-exponential scale for Theorems 2 & 3, where |delta_i| <= c_thm23 / 2.

Usage

score_diff_scales(lo, hi)

Arguments

lo

Numeric. Lower bound of score difference (usually a - b).

hi

Numeric. Upper bound of score difference (usually b - a).

Value

Named list with elements c_thm1 and c_thm23.

Details

Both conventions bound the same quantity: after centering, delta_i lies in [-(hi-lo)/2, (hi-lo)/2], so max|delta_i| = (hi-lo)/2, which equals both c_thm1 and c_thm23 / 2.

Examples

score_diff_scales(lo = -1, hi = 1)
#> $c_thm1
#> [1] 1
#> 
#> $c_thm23
#> [1] 2
#>