Title

    dftol -- Distribution-free tolerance intervals

Syntax

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

    options       Description
    -------------------------------------------------------------------------
      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