Title

dftol-- Distribution-free tolerance intervals

dftolvarname [if] [in],[conf(#)beta(#)rlowerdetail]

optionsDescription -------------------------------------------------------------------------conf(#)set confidence level of the tolerance interval; default isconf(95)beta(#)set percentage of the population covered by the tolerance interval; default isbeta(95)rlowercontrol how an odd number of blocks is removeddetaildisplay additional information -------------------------------------------------------------------------

dftolcomputes distribution-free tolerance intervals forvarnamefollowing the method proposed by Murphy (1948).

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

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

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

rlowerspecifies 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 byrthe number of blocks, ifris 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. Ifris 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.

detaildisplays 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).

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

dftolsaves the following inr():Scalars

r(lower)lower limit of the tolerance interval (omitted if exactly one block is removed withoutrlower)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 withoutrlower)r(upper)upper limit of the tolerance interval (omitted if exactly one block is removed withrlower)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 withrlower)r(removed)number of blocks removedr(actualconf)actual confidence level of the tolerance intervalIgnacio López de Ullibarri Department of Mathematics University of A Coruña, Spain E-mail: ilu@udc.es

Hahn G and Meeker WQ (1991),

Statistical Intervals, New York: Wiley & SonsJann B (2005),

moremata: Stata module (Mata) to provide variousfunctions, available from http://ideas.repec.org/c/boc/bocode/s455001.htmlMurphy RB (1948), Non-parametric tolerance limits,

Annals of Mathematical