------------------------------------------------------------------------------- help forgb2predStephen P. Jenkins (April 2004) -------------------------------------------------------------------------------

Prediction following fitting of a GB2 distribution

gb2pred[ifexp] [inrange] [,aval(value list1)bval(value list2)pval(value list3)qval(value list4)abpqval(value list)poorfrac(#)cdf(cdfname)pdf(pdfname)]

Description

gb2predcalculates statistics summarizing a 4 parameter Generalized Beta of the Second Kind distribution which has been fitted usinggb2fitto sample observations on variablevar.gb2predis usually used when the model parameters have been specified as functions of covariates ingb2fit. 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)andqval(valuelist4)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 ofvarless than the cut-off specified by#.

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

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

ifandinhave an effect only if optionscdfor

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

e(bba),e(bbb),e(bbp), ande(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)ande(pdfvar)are the variable names specified for the c.d.f. and the p.d.f.

e(mode),e(mean),e(var),e(sd), ande(i2)are the estimated mode, mean, variance, standard deviation, and half coefficient of variation squared.e(pX), ande(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)

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

Also seegb2fit