Sample Size for Nonparametric Confidence Interval for a Quantile

Compute the sample size necessary to achieve a specified confidence level for a nonparametric confidence interval for a quantile.

ciNparN(p = 0.5, lcl.rank = ifelse(ci.type == "upper", 0, 1), 
    n.plus.one.minus.ucl.rank = ifelse(ci.type == "lower", 0, 1), 
    ci.type = "two.sided", conf.level = 0.95)

Arguments

p

numeric vector of probabilities specifying the quantiles. All values of p must be between 0 and 1. The default value is p=0.5.

lcl.rank, n.plus.one.minus.ucl.rank

numeric vectors of non-negative integers indicating the ranks of the order statistics that are used for the lower and upper bounds of the confidence interval for the specified quantile(s). When lcl.rank=1 that means use the smallest value as the lower bound, when lcl.rank=2 that means use the second to smallest value as the lower bound, etc. When n.plus.one.minus.ucl.rank=1 that means use the largest value as the upper bound, when n.plus.one.minus.ucl.rank=2 that means use the second to largest value as the upper bound, etc. A value of 0 for lcl.rank indicates no lower bound (i.e., -Inf) and a value of 0 for n.plus.one.minus.ucl.rank indicates no upper bound (i.e., Inf). When
ci.type="upper" then lcl.rank is set to 0 by default, otherwise it is set to 1 by default. When ci.type="lower" then n.plus.one.minus.ucl.rank is set to 0 by default, otherwise it is set to 1 by default.

ci.type

character string indicating what kind of confidence interval to compute. The possible values are "two-sided" (the default), "lower", and "upper".

conf.level

numeric vector of numbers between 0 and 1 indicating the confidence level associated with the confidence interval(s). The default value is conf=0.95.

Details

If the arguments p, lcl.rank, n.plus.one.minus.ucl.rank and conf.level are not all the same length, they are replicated to be the same length as the length of the longest argument.

The help file for eqnpar explains how nonparametric confidence intervals for quantiles are constructed and how the confidence level associated with the confidence interval is computed based on specified values for the sample size and the ranks of the order statistics used for the bounds of the confidence interval.

The function ciNparN determines the required the sample size via a nonlinear optimization.

Value

numeric vector of sample sizes.

References

See the help file for eqnpar.

Author

Steven P. Millard (EnvStats@ProbStatInfo.com)

Note

See the help file for eqnpar.

Examples

  # Look at how the required sample size for a confidence interval 
  # increases with increasing confidence level for a fixed quantile:

  seq(0.5, 0.9, by = 0.1) 
#> [1] 0.5 0.6 0.7 0.8 0.9
  #[1] 0.5 0.6 0.7 0.8 0.9 

  ciNparN(p = 0.9, conf.level=seq(0.5, 0.9, by = 0.1)) 
#> [1]  7  9 12 16 22
  #[1]  7  9 12 16 22

  #----------

  # Look at how the required sample size for a confidence interval increases 
  # as the quantile moves away from 0.5:

  ciNparN(p = seq(0.5, 0.9, by = 0.1)) 
#> [1]  6  7  9 14 29
  #[1]  6  7  9 14 29