Contaminated-sample bounds for a recorded proportion

A recorded distribution is a mixture of the clean distribution of interest and an unknown contaminant (mis-coded offences, unfounded records, wrong addresses) in a known share p. For any event the clean probability lies in \([\max(0, (q-p)/(1-p)),\; \min(1, q/(1-p))]\) with \(q\) the recorded probability; both ends are attained, the width is \(p/(1-p)\), and the interval is narrower than the unit interval exactly when \(p < q\) or \(p < 1-q\) (Research.P11.clean_bounds, clean_lower_attained, clean_upper_attained, clean_width, clean_informative; Manski sec. 5.2).

Usage

morie_contaminated_bounds(q, p)

Arguments

q

Recorded probability (or vector of them) of the event.

p

Known contamination share in [0, 1).

Value

A data frame with q, lower, upper, width (before clipping to [0, 1]), informative and attribute "theorems".

Examples

morie_contaminated_bounds(q = c(0.05, 0.3, 0.6), p = 0.1)
#>      q     lower      upper     width informative
#> 1 0.05 0.0000000 0.05555556 0.1111111        TRUE
#> 2 0.30 0.2222222 0.33333333 0.1111111        TRUE
#> 3 0.60 0.5555556 0.66666667 0.1111111        TRUE