Sheppa28

beta prime distribution

Hi. I think you mix up some things... the Dagum distribution as defined in http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/VGAM/html/dagum.html does not have the Beta function in the quotient, hence cannot be a special case of the generalized beta prime distribution. regards. —Preceding unsigned comment added by 129.132.146.66 (talk) 13:13, 16 March 2011 (UTC)

Thanks for your message, but the relationship is indeed correct. The probability density function follow as

${\begin{aligned}\beta ^{'}(p,1,a,b)&={\frac {a{\left({\frac {x}{b}}\right)}^{ap-1}\left({1+{\left({\frac {x}{b}}\right)}^{a}}\right)^{-p-1}}{b\beta (p,1)}}\\&=ab^{-ap}px^{-1+ap}{\left(1+{\left({\frac {x}{b}}\right)}^{a}\right)}^{-1-p}\\&={\textrm {Dagum}}(p,a,b)\\\end{aligned}}$

Where $\beta (\alpha ,\beta )\,$ is the beta function, and $\beta (p,1)={\tfrac {1}{p}}\,$.

Sheppa28 (talk) 17:18, 16 March 2011 (UTC)

ah, you are right. i didnt look properly and thought the alpha and beta parameters correspond to a and b in dagum... sorry for the inconveniences. regards. —Preceding unsigned comment added by 129.132.146.66 (talk) 08:05, 17 March 2011 (UTC)

No worries. Have a good day! Sheppa28 (talk) 10:45, 17 March 2011 (UTC)

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