hypertolint: Hypergeometric Tolerance Intervals

In tolerance: Statistical Tolerance Intervals and Regions

Hypergeometric Tolerance Intervals

Description

Provides 1-sided or 2-sided tolerance intervals for hypergeometric random variables. From a sampling without replacement perspective, these limits use the proportion of units from group A (e.g., "black balls" in an urn) in a sample to bound the number of potential units drawn from group A in a future sample taken from the universe.

Usage

hypertol.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 from group A in the sample. Can be a vector, in which case the sum of x is used.
n	The size of the random sample of units selected.
N	The population size.
m	The quantity of units 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

hypertol.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 n/N.
p.hat	The proportion of units in the sample from group A, calculated by x/n.
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. Also, compare the functionality of this procedure with the acc.samp procedure, which is to determine a minimal acceptance limit for a particular sampling plan.

References

Brown, L. D., Cai, T. T., and DasGupta, A. (2001), Interval Estimation for a Binomial Proportion, Statistical Science, 16, 101–133.

Eichenberger, P., Hulliger, B., and Potterat, J. (2011), Two Measures for Sample Size Determination, Survey Research Methods, 5, 27–37.

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

See Also

acc.samp, Hypergeometric

Examples

 
## 90%/95% 1-sided and 2-sided hypergeometric tolerance 
## intervals for a future sample of 30 when the universe
## is of size 100.

hypertol.int(x = 15, n = 50, N = 100, m = 30, alpha = 0.10, 
             P = 0.95, side = 1, method = "LS")
hypertol.int(x = 15, n = 50, N = 100, m = 30, alpha = 0.10, 
             P = 0.95, side = 1, method = "CC")
hypertol.int(x = 15, n = 50, N = 100, m = 30, alpha = 0.10, 
             P = 0.95, side = 2, method = "LS")
hypertol.int(x = 15, n = 50, N = 100, m = 30, alpha = 0.10, 
             P = 0.95, side = 2, method = "CC")
 

tolerance documentation built on May 29, 2024, 7:38 a.m.