How to implement random draws from a dagum distribution?

[FlorianRoth]

Hi Statalisters,

I have grouped income data and used dagfit to fit a dagum distribution to this data. From this I get the the parameter estiamtes for a,b and p. Now I would like draw a random sample N from this the fitted dagum distribution. If I understand correctly this can be done using inverse transformation sampling. After I load the data into Stata my code looks as follows:

dagfit nbtotal, z1(bracketbeg) z2(bracketend)

gen b = e(bb)
gen a = e(ba)
gen p = e(bp)
keep a b p
duplicates drop

expand 1000 // size of random sample
gen runif=runiform()
gen randomdagum = (1 + (runif/e(bb))^-1*e(ba))^e(bp) // inverse CDF of a Dagum Distribution

Would you consider this to be the correct way to do this?

Best regards,
Florian

[Stephen Jenkins]

[duplicate post]. I haven't checked your specific code, but use of the inversion approach seems fine in principle to me

[Michal Brzezinski]

Dear Florian,

your formula for random Dagum variates wron uses a reciprocal of Dagum CDF, not the inverse of the CDF. The inverse, that is quantile function, is:
F^-1(u) = b(u^-1/p -1)^-1/a, where u is uniform variate generated by runiform().

Hope this helps,
Michal