help jnsw                                                Version 1.0 2007-02-26
-------------------------------------------------------------------------------


Title

    jnsw --  Fit Johnson's system of transformations by Wheeler's quantile
             method


Syntax

        jnsw varname [if] [in] [, options]

    options               Description
    -------------------------------------------------------------------------
    Main
      generate(newvar)    create variable named newvar that is the fitted
                            normal transformation of varname
      distribution(type)  force fit to a specified Johnson distribution type
      lntolerance(#)      tolerance for discriminating from the log-normal
                            line
      tboneonly           use only the upper quantiles
      percentile(#)       use a subset of the data
      gamma(#)            force fit with a specified value for gamma
      delta(#)            force fit with a specified value for delta
      lambda(#)           force fit with a specified value for lambda
      xi(#)               force fit with a specified value for xi
    -------------------------------------------------------------------------
    by may be used with jnsw; see by.


Description

    jnsw fits Johnson systems of transformations using the quantile method of
    Wheeler (1980).


Options

        +------+
    ----+ Main +-------------------------------------------------------------

    distribution forces the fit to a user-specified Johnson distribution
        type; acceptable types are SL, SB and SU in upper case, lower case or
        mixed case.  The default is to select the type by reference to the
        log-normal line.

    lntolerance specifies the tolerance for discriminating SB and SU
        distribution types from SL, based upon difference from the log-normal
        line.  The default is 0.01, acceptable values are 0.0001 to 0.5, with
        smaller values resulting in more fits declared as SL type.

    tboneonly requests that only the upper tail contribute to the the
        intermediary tb result; the default is to use the average of two tbs
        determined from both tails.

    percentile(#) requests that only the values of varname less than or equal
        to the # percentile contribute to the fit; the default is 100.

    gamma delta lambda delta forces to fit to use user-specified values of
        the parameter.


Remarks

    jnsw fits parameters of Johnson distributions by the method of quantiles
    (Wheeler, 1980).  The method selects and fits the Johnson distribution on
    the basis of five quantiles, one of which is the median.  Flynn (2006)
    determined that, at least for fitting certain SB distributions, Wheeler's
    quantile method performs better than two other popular percentile methods
    that use only four percentiles.

    Details of the method for fitting gamma and delta are given in Wheeler
    (1980).  In particular, the default of using both tails to calculate the
    intermediary statistic, tb, is based upon a suggestion in the article
    that this is expected to provide for more accurate results in fitting
    delta.  The article illustrates the method using tb estimated from only
    one tail, however, and the tboneonly option will force this should the
    user desire to follow Wheeler's illustrations.

    lambda and xi are fit using ordinary least-squares linear regression, as
    suggested in the article.

    The percentile option is made available for use with censored data, as
    suggested in the article.

    For the SL Johnson type, jnsw deviates from the article in that (i) gamma
    is explicitly fit (Wheeler combines it into delta, assuming lambda will
    be explicitly fit), (ii) delta is constrained to be positive in
    accordance with convention (Wheeler allows it to be negative for
    negatively skewed data, again, assuming that lambda will be allowed to
    vary freely), and (iii) lambda is set to 1 if the data are positively
    skewed and -1 if the data are negatively skewed.  This latter convention
    of constraining lambda to unity, with its sign reflecting direction of
    skew, follows Hill, Hill and Holder (1976).  That method is implemented
    in jnsn (if installed).  These deviations from Wheeler's article allow
    results between the two methods to be directly comparable.  They also
    allow the results from jnsw, which are returned in return scalars and a
    return macro, to be used in conjunction with ajv (if installed) to
    generate random variates that follow the Johnson distribution fit for 
    varname by jnsw.

References

    M. R. Flynn, Fitting human exposure data with the Johnson SB
    distribution. Journal of Exposure Science and Environmental Epidemiology
    16:56–62, 2006.

    I. D. Hill, R. Hill and R. L. Holder, Fitting Johnson curves by moments.
    Applied Statistics 25:180–89, 1976.

    R. E. Wheeler, Quantile estimators of Johnson curve parameters.
    Biometrika 67:725–28, 1980.

Examples

    . jnsw x

    . jnsw x, di(sb) p(75) l(101) x(0)


Author

    Joseph Coveney jcoveney@bigplanet.com


Also see

    Manual:  [R] summarize, [R] boxcox, [R] lnskew0, [R] ladder

    Online:  jnsn, ajv, transint, summarize, boxcox, lnskew0, ladder, xriml