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help for hdquantile
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Harrell-Davis estimator of quantiles

        hdquantile varlist [if exp] [in range] , generate(newvarlist) [ a(#)
                 by(byvarlist) ]

        hdquantile varlist [if exp] [in range] , p(numlist) [
                 matname(matrix_name) matrix_list_options ]

        hdquantile varname [if exp] [in range] , p(numlist) [ by(byvarlist)
                 matname(matrix_name) matrix_list_options ]


Description

    hdquantile estimates quantiles using the method of Harrell and Davis
    (1982). There are two main syntaxes, depending on which of the generate()
    and p() options is specified.

    If the option generate() is specified, as many quantiles are there are
    non-missing values for all the variables specified are estimated. Given n
    order statistics y_(i) such that y_(1) <= ... <= y_(n), quantiles are
    calculated at the plotting positions (i - a)/(n - 2a + 1), where a may be
    tuned using the a() option. By default a = 0.5. The by() option is
    permissible with this syntax.

    If the option p() is specified, selected quantiles for the percent points
    in p() are estimated and displayed (and optionally saved) as a matrix.
    This matrix may be either for one or more variables or for one variable
    grouped according to the by() option.

Remarks

    The quantile for cumulative proportion p is estimated as a weighted mean
    of all order statistics y_(i) with weights

        ibeta((n + 1)p, (n + 1)(1 - p), i/n) - ibeta((n + 1)p, (n + 1)(1 -
        p), (i - 1)/n)

    See ibeta().


Options

    Either generate() or p() must be specified.

    generate() specifies the names of as many new variables as there are
        variables in varlist to hold estimates of quantiles.

        a() specifies a in the formula for plotting position. The default is
        a = 0.5, giving (i - 0.5) / n. Other choices include a = 0, giving
        i / (n + 1), and a = 1/3, giving (i - 1/3) / (n + 1/3).  This is
        relevant only with generate().

    p() specifies one or more integers between 1 and 99 indicating percent
        points (plotting positions) for which quantiles should be estimated.
        Thus p(25(25)75) specifies estimation for the 25%, 50% and 75%
        percent points, or for plotting positions 0.25, 0.50, 0.75.

        matname() specifies the name of a matrix in which to save the results
        of calculations. This is relevant only with p().

        matrix_list_options are options of matrix list tuning the display of
        the matrix of quantiles. This is relevant only with p().

    by() specifies one or more variables defining distinct groups for which
        quantiles should be estimated. Under by() the group size n and the
        ranking from 1 to n are determined within each group.


Examples 

    . hdquantile length width height, gen(Qlength Qwidth Qheight)

    . hdquantile length, by(grade) gen(Qlength)

    . hdquantile length, p(10 25 50 75 90)

    . hdquantile length, p(10 25 50 75 90) m(Qmatrix)


Author

    Nicholas J. Cox, University of Durham, U.K.
    n.j.cox@durham.ac.uk


References

    Harrell, F.E. and C.E. Davis. 1982.  A new distribution-free quantile
        estimator.  Biometrika 69: 635-640.

    Sheather, S.J. and J.S. Marron. 1990.  Kernel quantile estimators.
        Journal, American Statistical Association 85: 410-416.

    Dielman, T.E., C. Lowry and R. Pfaffenberger.  1994. A comparison of
        quantile estimators.  Communications in Statistics - Simulation and
        Computation 23: 355-371.

    Hutson, A.D. and M.D. Ernst. 2000.  The exact bootstrap mean and variance
        of an L-estimator.  Journal, Royal Statistical Society B 62: 89-94.

    Ernst, M.D. and A.D. Hutson. 2003.  Utilizing a quantile function
        approach to obtain exact bootstrap solutions.  Statistical Science
        18: 231-240.


Also see 

    Online:  help for qplot (if installed)