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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)"
#>