# umatolint: Uniformly Most Accurate Upper Tolerance Limits for Certain... In tolerance: Statistical Tolerance Intervals and Regions

## Description

Provides uniformly most accurate upper tolerance limits for the binomial, negative binomial, and Poisson distributions.

## Usage

 ```1 2``` ```umatol.int(x, n = NULL, dist = c("Bin", "NegBin", "Pois"), N, alpha = 0.05, P = 0.99) ```

## Arguments

 `x` A vector of data which is distributed according to one of the binomial, negative binomial, or Poisson distributions. If the length of `x` is 1, then it is assumed that this number is the sum of iid values from the assumed distribution. `n` The sample size of the data. If `null`, then `n` is calculated as the length of `x`. `dist` The distribution for the data given by `x`. The options are `"Bin"` for the binomial distribution, `"NegBin"` for the negative binomial distribution, and `"Pois"` for the Poisson distribution. `N` Must be specified for the binomial and negative binomial distributions. If `dist = "Bin"`, then `N` is the number of Bernoulli trials and must be a positive integer. If `dist = "NegBin"`, then `N` is the total number of successful trials (or dispersion parameter) and must be strictly positive. `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.

## Value

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

 `alpha` The specified significance level. `P` The proportion of the population covered by this tolerance interval. `p.hat` The maximum likelihood estimate for the probability of success in each trial; reported if `dist = "Bin"`. `nu.hat` The maximum likelihood estimate for the probability of success in each trial; reported if `dist = "NegBin"`. `lambda.hat` The maximum likelihood estimate for the rate of success; reported if `dist = "Pois"`. `1-sided.upper` The 1-sided upper tolerance limit.

## References

Zacks, S. (1970), Uniformly Most Accurate Tolerance Limits for Monotone Likelihood Ratio Families of Discrete Distributions, Journal of the American Statistical Association, 65, 307–316.

`Binomial`, `NegBinomial`, `Poisson`
 ```1 2 3 4 5 6 7 8``` ``` ## Examples from Zacks (1970). umatol.int(25, n = 4, dist = "Bin", N = 10, alpha = 0.10, P = 0.95) umatol.int(13, n = 10, dist = "NegBin", N = 2, alpha = 0.10, P = 0.95) umatol.int(37, n = 10, dist = "Pois", alpha = 0.10, P = 0.95) ```