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help for smpred                                 Stephen P. Jenkins (April 2004)
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Prediction following fitting of a Singh-Maddala distribution

        smpred [if exp] [in range] [, aval(value list1) bval(value list2)
                 qval(value list3) abqval(value list) poorfrac(#)
                 cdf(cdfname) pdf(pdfname) ]

Description

    smpred calculates statistics summarizing a 3 parameter Singh-Maddala
    distribution which has been fitted using smfit to a distribution of
    sample observations on variable var.  smpred is usually used when the
    model parameters have been specified as functions of covariates using
    smfit. Users specify particular covariate values here, 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 selected quantiles, cumulative shares of total income at
    quantiles (i.e. the Lorenz curve ordinates), the mode, mean, standard
    deviation, variance, half the coefficient of variation squared, Gini
    coefficient, and quantile ratios p90/p10, p75/p25. The command can be
    repeated using a different set of covariate values.

Options

    aval(value list1), bval(value list2), and qval(value list3) 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.

    abqval(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
        Singh-Maddala c.d.f. value F(x) for each x.

    pdf(pdfname) creates a new variable pdfname containing the estimated
        Singh-Maddala 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), and e(bbq) are the estimated Singh-Maddala 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), e(i2), and e(gini) are the estimated
    mode, mean, variance, standard deviation, half coefficient of variation
    squared, Gini coefficient. 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


    . smfit x

    . smpred

    . smfit x, a(age sex) b(age sex) q(age sex)

    . smpred, a(40,2,1) b(40,2,1) q(40,2,1)

    . smpred, abq(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

smfit