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help for gb2pred                                Stephen P. Jenkins (April 2004)
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Prediction following fitting of a GB2 distribution

        gb2pred [if exp] [in range] [ , aval(value list1) bval(value list2)
                 pval(value list3) qval(value list4) abpqval(value list)
                 poorfrac(#) cdf(cdfname) pdf(pdfname) ]

Description

    gb2pred calculates statistics summarizing a 4 parameter Generalized Beta
    of the Second Kind distribution which has been fitted using gb2fit to
    sample observations on variable var.  gb2pred is usually used when the
    model parameters have been specified as functions of covariates in
    gb2fit. Here users specify particular covariate values, which implies
    values of the model parameters, and thence statistics can be calculated,
    together with the fitted c.d.f. and p.d.f. The statistics produced by
    default are quantiles, Lorenz ordinates, the mode, mean, standard
    deviation, variance, and half the coefficient of variation squared. The
    command can be repeated using a different set of covariate values.

Options

    aval(value list1), bval(value list2), pval(value list3) and qval(value
        list4) are required if the original model was estimated with
        covariates. In this case, the user must specify a value for each
        covariate included in the original model, and in the same order. The
        last element in each equation must always be 1 (corresponding to the
        intercept term). Where there is more than one element per equation,
        they must be separated by commas.

    abpqval(value list) can be used instead of the previous option if the
        same covariates appeared in each parameter equation.

    poorfrac(#) displays the estimated proportion with values of var less
        than the cut-off specified by #.

    cdf(cdfname) creates a new variable cdfname containing the estimated GB2
        c.d.f. value F(x) for each x.

    pdf(pdfname) creates a new variable pdfname containing the estimated GB2
        p.d.f. value f(x) for each x.

        Options if and in have an effect only if options cdf or pdf are
        specified.


Saved results

    The following are saved, some contingent on the relevant options being
    specified:

    e(bba), e(bbb), e(bbp), and e(bbq) are the estimated GB2 parameters. (If
    the original model included no covariates, these contain the parameters
    originally estimated. If covariates were included, these contain the
    parameters evaluated at the values of the covariates specified here.)


    e(cdfvar) and e(pdfvar) are the variable names specified for the c.d.f.
    and the p.d.f.

    e(mode), e(mean), e(var), e(sd), and e(i2) are the estimated mode, mean,
    variance, standard deviation, and half coefficient of variation squared.
    e(pX), and e(LpX) are the quantiles, and Lorenz ordinates, where X = {1,
    5, 10, 20, 25, 30, 40, 50, 60, 70, 75, 80, 90, 95, 99}.


Examples

    . gb2fit x

    . gb2pred

    . gb2fit x, a(age sex) b(age sex) p(age sex) q(age sex)

    . gb2pred, a(40,2,1) b(40,2,1) p(40,2,1) q(40,2,1)

    . gb2pred, abpq(50,2,1) poorfrac(100)


Author

    Stephen P. Jenkins <stephenj@essex.ac.uk>, Institute for Social and
    Economic Research, University of Essex, Colchester CO4 3SQ, U.K.


Also see

gb2fit