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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

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