# cautolint: Cauchy Tolerance Intervals In tolerance: Statistical Tolerance Intervals and Regions

## Description

Provides 1-sided or 2-sided tolerance intervals for Cauchy distributed data.

## Usage

 `1` ```cautol.int(x, alpha = 0.05, P = 0.99, side = 1) ```

## Arguments

 `x` A vector of data which is Cauchy distributed. `alpha` The level chosen such that `1-alpha` is the confidence level. `P` The proportion of the population to be covered by this tolerance interval. `side` Whether a 1-sided or 2-sided tolerance interval is required (determined by `side = 1` or `side = 2`, respectively).

## Value

`cautol.int` returns a data.frame with items:

 `alpha` The specified significance level. `P` The proportion of the population covered by this tolerance interval. `1-sided.lower` The 1-sided lower tolerance bound. This is given only if `side = 1`. `1-sided.upper` The 1-sided upper tolerance bound. This is given only if `side = 1`. `2-sided.lower` The 2-sided lower tolerance bound. This is given only if `side = 2`. `2-sided.upper` The 2-sided upper tolerance bound. This is given only if `side = 2`.

## References

Bain, L. J. (1978), Statistical Analysis of Reliability and Life-Testing Models, Marcel Dekker, Inc.

`Cauchy`
 ``` 1 2 3 4 5 6 7 8 9 10``` ``` ## 95%/90% 2-sided Cauchy tolerance interval for a sample ## of size 1000. set.seed(100) x <- rcauchy(1000, 100000, 10) out <- cautol.int(x = x, alpha = 0.05, P = 0.90, side = 2) out plottol(out, x, plot.type = "both", x.lab = "Cauchy Data") ```