# neghypertolint: Negative Hypergeometric Tolerance Intervals In tolerance: Statistical Tolerance Intervals and Regions

## Description

Provides 1-sided or 2-sided tolerance intervals for negative hypergeometric random variables. When sampling without replacement, these limits are on the total number of expected draws in a future sample in order to achieve a certain number from group A (e.g., "black balls" in an urn).

## Usage

 ```1 2``` ```neghypertol.int(x, n, N, m = NULL, alpha = 0.05, P = 0.99, side = 1, method = c("EX", "LS", "CC")) ```

## Arguments

 `x` The number of units drawn in order to achieve `n` successes. Can be a vector, in which case the sum of `x` is used. `n` The target number of successes in the sample drawn (e.g., the number of "black balls" you are to draw in the sample). `N` The population size (e.g., the total number of balls in the urn). `m` The target number of successes to be sampled from the universe for a future study. If `m = NULL`, then the tolerance limits will be constructed assuming `n` for this quantity. `alpha` The level chosen such that `1-alpha` is the confidence level. `P` The proportion of units from group A in future samples of size `m` 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). `method` The method for calculating the lower and upper confidence bounds, which are used in the calculation of the tolerance bounds. The default method is `"EX"`, which is an exact-based method. `"LS"` is the large-sample method. `"CC"` gives a continuity-corrected version of the large-sample method.

## Value

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

 `alpha` The specified significance level. `P` The proportion of units from group A in future samples of size `m`. `rate` The sampling rate determined by `x/N`. `p.hat` The proportion of units in the sample from group A, calculated by `n/x`. `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`.

## Note

As this methodology is built using large-sample theory, if the sampling rate is less than 0.05, then a warning is generated stating that the results are not reliable.

## References

Khan, R. A. (1994), A Note on the Generating Function of a Negative Hypergeometric Distribution, Sankhya: The Indian Journal of Statistics, Series B, 56, 309–313.

Young, D. S. (2014), Tolerance Intervals for Hypergeometric and Negative Hypergeometric Variables, Sankhya: The Indian Journal of Statistics, Series B, 77(1), 114–140.

`acc.samp`, `NegHypergeometric`
 ```1 2 3 4 5 6 7 8``` ```## 90%/95% 2-sided negative hypergeometric tolerance ## intervals for a future number of 20 successes when ## the universe is of size 100. The estimates are ## based on having drawn 50 in another sample to achieve ## 20 successes. neghypertol.int(50, 20, 100, m = 20, alpha = 0.05, P = 0.95, side = 2, method = "LS") ```