*! version 1.1.1 20jan2013

Title

dftol -- Distribution-free tolerance intervals

Syntax

dftol varname [if] [in] , [conf(#) beta(#) rlower detail]

conf(#) set confidence level of the tolerance interval; default is conf(95)

beta(#) set percentage of the population covered by the tolerance interval; default is beta(95)

rlower control how an odd number of blocks is removed

detail display additional information

Description

dftol computes distribution-free tolerance intervals for varname following the method proposed by Murphy (1948).

Remarks

dftol requires that the Stata module -moremata- (Jann, 2005) be installed.

Options

conf(#) specifies the confidence level of the tolerance interval as a percentage. The default is conf(95), meaning a 95% confidence level.

beta(#) specifies the percentage of the sampled population to be contained in the tolerance interval. The default is beta(95), meaning a percentage equal to 95%.

rlower specifies the way the blocks are removed from the left and right ends of the ordered sample, when an odd number of blocks is to be
removed. Denoting by r the number of blocks, if r is an odd number and this option is used, then (r-1)/2 and (r+1)/2 blocks
are removed from the left and right ends, respectively. If r is an even number this option has no effect and exactly the same number of blocks
are removed from each end (see Hahn and Meeker, 1991). To better understand the name chosen for the option, note that when only one block is removed
(r=1) the result is a lower bound (i.e., a tolerance interval whose right limit is infinity) if the option is used, and an upper bound (i.e., a
tolerance interval whose left limit is minus infinity) if the option is not used.

detail displays auxiliary information. The following items are printed: a) Index(es) of the observation(s) defining the interval, b) number of blocks
removed and c) actual confidence level. Note that even is this option is not used, the information is always saved and may be recovered from the saved results
(see below and also [P] return).

Examples

. sysuse auto
. dftol price
. dftol price, c(99) b(99)
. dftol price, b(90)
. dftol price, b(90) nulower
. dftol price, detail

Saved results

dftol saves the following in r():

Scalars

r(lower) lower limit of the tolerance interval (omitted if exactly one block is removed without rlower)

r(indexlower) index of the observation of the ordered sample giving the lower limit of the tolerance interval
(omitted if exactly one block is removed without rlower)

r(upper) upper limit of the tolerance interval (omitted if exactly one block is removed with rlower)

r(indexupper) index of the observation of the ordered sample giving the upper limit of the tolerance interval
(omitted if exactly one block is removed with rlower)

r(removed) number of blocks removed

r(actualconf) actual confidence level of the tolerance interval

Author

Ignacio López de Ullibarri

Department of Mathematics

University of A Coruña, Spain

E-mail: ilu@udc.es

References

Hahn G and Meeker WQ (1991), Statistical Intervals, New York: Wiley & Sons

Jann B (2005), moremata: Stata module (Mata) to provide various functions, available from http://ideas.repec.org/c/boc/bocode/s455001.html

Murphy RB (1948), Non-parametric tolerance limits, Annals of Mathematical Statistics, 19: 581-589