Probability Integral Transform (PIT)

If X ~ F, then F(X) ~ Uniform(0,1). Returned U should be approx uniform if the assumed F is correct. Attaches a KS p-value of U against Uniform(0,1) as the diagnostic for fit quality.

Usage

mrm_pit(sample, dist = "norm", ...)

Arguments

sample

Numeric vector.

dist

Distribution suffix for p<dist>.

...

Additional parameters for p<dist>.

Value

data.frame with raw, U columns and attributes ks_stat, ks_pvalue.

Examples

set.seed(2026)
x <- rnorm(200)
# Under correct distributional assumption, U should be ~Uniform(0,1):
pit <- mrm_pit(x, dist = "norm")
attr(pit, "ks_pvalue") # large p-value => no evidence against fit
#> [1] 0.9730582
# If we deliberately misspecify (claim t_3 fits the normal sample):
pit_wrong <- mrm_pit(x, dist = "t", df = 3)
attr(pit_wrong, "ks_pvalue") # small p-value => misspecification detected
#> [1] 0.1816978