{smcl}
{* April 2004}{...}
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help for {hi:gb2pred}{right:Stephen P. Jenkins (April 2004)}
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{title:Prediction following fitting of a GB2 distribution}
{p 8 17 2}{cmd:gb2pred} [{cmd:if} {it:exp}] [{cmd:in} {it:range}] [ {cmd:,}
{cmdab:a:val(}{it:value list1}{cmd:)} {cmdab:b:val(}{it:value list2}{cmd:)}
{cmdab:p:val(}{it:value list3}{cmd:)} {cmdab:q:val(}{it:value list4}{cmd:)}
{cmdab:abpq:val(}{it:value list}{cmd:)} {cmdab:poor:frac(}{it:#}{cmd:)}
{cmdab:cdf(}{it:cdfname}{cmd:)} {cmdab:pdf(}{it:pdfname}{cmd:)} ]
{title:Description}
{p 4 4 2}
{cmd:gb2pred} calculates statistics summarizing a 4 parameter
Generalized Beta of the Second Kind distribution which has been fitted
using {cmd:gb2fit} to sample observations on variable {it:var}.
{cmd:gb2pred} is usually used when the model parameters have been specified as functions of
covariates in {cmd: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.
{title:Options}
{p 4 8 2}{cmd:aval(}{it:value list1}{cmd:)}, {cmd:bval(}{it:value list2}{cmd:)},
{cmd:pval(}{it:value list3}{cmd:)} and
{cmd:qval(}{it:value list4}{cmd:)} 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.
{p 4 8 2}{cmd:abpqval(}{it:value list}{cmd:)} can be used instead of the previous option
if the same covariates appeared in each parameter equation.
{p 4 8 2}{cmd:poorfrac(}{it:#}{cmd:)} displays the estimated proportion with values of {it:var}
less than the cut-off specified by {it:#}.
{p 4 8 2}{cmd:cdf(}{it:cdfname}{cmd:)} creates a new variable {it:cdfname} containing the
estimated GB2 c.d.f. value F(x) for each x.
{p 4 8 2}{cmd:pdf(}{it:pdfname}{cmd:)} creates a new variable {it:pdfname} containing the
estimated GB2 p.d.f. value f(x) for each x.
{p 8 8 2}Options {cmd:if} and {cmd:in} have an effect only if options {cmd:cdf} or {cmd:pdf} are specified.
{title:Saved results}
{p 4 4 2}The following are saved, some contingent on the relevant options being specified:
{p 4 4 2}{cmd:e(bba)}, {cmd:e(bbb)}, {cmd:e(bbp)}, and {cmd: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.)
{p 4 4 2}{cmd:e(cdfvar)} and {cmd:e(pdfvar)} are the variable names specified for the
c.d.f. and the p.d.f.
{p 4 4 2}
{cmd:e(mode)}, {cmd:e(mean)}, {cmd:e(var)}, {cmd:e(sd)}, and {cmd:e(i2)}
are the estimated mode, mean, variance, standard deviation, and half coefficient of
variation squared. {cmd:e(pX)}, and {cmd: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}.
{title:Examples}
{p 4 8 2}{inp:. gb2fit x }
{p 4 8 2}{inp:. gb2pred }
{p 4 8 2}{inp:. gb2fit x, a(age sex) b(age sex) p(age sex) q(age sex)}
{p 4 8 2}{inp:. gb2pred, a(40,2,1) b(40,2,1) p(40,2,1) q(40,2,1) }
{p 4 8 2}{inp:. gb2pred, abpq(50,2,1) poorfrac(100) }
{title:Author}
{p 4 4 2}Stephen P. Jenkins , Institute for Social
and Economic Research, University of Essex, Colchester CO4 3SQ, U.K.
{title:Also see}
{help gb2fit}