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help for tkdensity
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Univariate kernel density estimation, calculation on transformed scale 

        tkdensity varname [if exp] [in range] [, generate(newvar_x newvar_d)
                 trans(transformation) graphopts(line_opts) kdensity_options
                 ]


Description

    tkdensity estimates and graphs kernel density estimates for the density
    function of numeric variable varname, doing the calculations on a
    specified transformed scale and back-transforming to show density versus
    the original scale. It is a convenience wrapper for kdensity.

Remarks

    For a monotone transformation t(x) the principle is that for densities f

        estimate of f{x} = estimate of f{t(x)} * |dt/dx|.

    For discussion and references, see Cox (2004, pp.76-78).

    On cube roots, see also Cox (2011).


Options 

    trans() specifies the transformation to be used. Transformations
        implemented are

        natural logarithm, which may be specified by ln or logarithm, and
        which is the default; for this values must all be strictly positive
        (>0);

        cube root, which may be specified by cube root; for this values may
        be negative, zero, or positive;

        square root, which may be specified by root or square root; for this
        values must all be zero or positive;

        reciprocal, which may be specified by reciprocal; for this values
        must all be strictly positive (>0);

        logit, which may be specified by logit; for this values must all be
        within (0,1) (and so not equal to 0 or 1).

        See underlining above for permitted abbreviations of keywords.

    generate() stores the results of the estimation.  newvar_x will contain
        the points at which the density is estimated.  newvar_d will contain
        the density estimate.

    graphopts(line_options) specifies options of line used to tune the
        graphical display of the density.

    kdensity_options are options of kdensity. Note that kdensity is called
        with option nograph and that in any case the density estimates it
        would graph would be on the transformed scale, so graphics options
        are excluded here. See also the option just above.  Note also that
        bandwidths are measured on the transformed scale.


Examples 

    . sysuse auto, clear

    . tkdensity mpg, trans(ln) kernel(biweight) bw(0.25)


Author

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


References 

    Cox, N.J. 2004.  Graphing distributions.  Stata Journal 2: 66-88. See
        esp. pp.76-78.
        http://www.stata-journal.com/sjpdf.html?articlenum=gr0003

    Cox, N.J. 2011.  Stata tip 96: Cube roots.  Stata Journal 11: 149-154.


Also see 

    kdensity