Closed-form Wilks (1941) tolerance-interval probability that the
sample interval from min(x) to max(x) covers at least coverage of the
population. Gibbons & Chakraborti Ch 2.11.
Usage
morie_tolerance_limits(x, coverage = 0.9, confidence = 0.95)
Arguments
- x
Numeric vector.
- coverage
Desired population coverage beta (default 0.90).
- confidence
Desired confidence (default 0.95).
Value
Named list: lower, upper, coverage_requested,
confidence_achieved, n, method.
Details
P(coverage of (X_(1), X_(n)) >= beta) =
1 - n * beta^(n-1) + (n - 1) * beta^n
References
Wilks (1941); Gibbons & Chakraborti (6e) Ch 2.11.
Examples
morie_tolerance_limits(1:100, coverage = 0.90, confidence = 0.95)
#> $lower
#> [1] 1
#>
#> $upper
#> [1] 100
#>
#> $coverage_requested
#> [1] 0.9
#>
#> $confidence_achieved
#> [1] 0.9996783
#>
#> $n
#> [1] 100
#>
#> $method
#> [1] "Distribution-free tolerance limits (Wilks)"
#>