quantileWilks {mistral}

Computing quantiles with the Wilks formula

Description

From the Wilks formula, compute a quantile (or a tolerance interval) with a given confidence level from a i.i.d. sample, or compute the minimal sample size to estimate a quantile (or a tolerance interval) with a given confidence level.

Usage

quantileWilks(alpha=0.95,beta=0.95,data=NULL,bilateral=FALSE)

Arguments

alpha

level of the unilateral or bilateral quantile (default = 0.95)

beta

level of the confidence interval on quantile value(s) (default = 0.95)

data

the data sample (vector format) to compute the quantile(s); if data=NULL (by default), the function returns the minimal sample size to compute the required quantile

bilateral

TRUE for bilateral quantile (default = unilateral = FALSE)

Value

4 output values if 'data' is specified; 1 output value (nmin) if 'data' is not specified

lower

lower bound of the bilateral tolerance interval; if bilateral=FALSE, no value

upper

upper bound of the tolerance interval (bilateral case) or quantile value (unilateral case)

nmin

minimal size of the required i.i.d. sample for given alpha and beta: - bilateral case: tolerance interval will be composed with the min and max of the sample; - unilateral case: the quantile will correspond to max of the sample.

ind

the index (unilateral case) or indices (bilateral case) of the quantiles in the ordered sample (increasing order)

Author(s)

Claire Cannamela and Bertrand Iooss

References

H.A. David and H.N. Nagaraja. Order statistics, Wiley, 2003.

W.T. Nutt and G.B. Wallis. Evaluation of nuclear safety from the outputs of computer codes in the presence of uncertainties. Reliability Engineering and System Safety, 83:57-77, 2004.

S.S. Wilks. Determination of Sample Sizes for Setting Tolerance Limits. Annals Mathematical Statistics, 12:91-96, 1941.

Examples

 
N <- quantileWilks(alpha=0.95,beta=0.95)
print(N)