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From |
Francisco Augusto <francisco.augusto.7@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: An application of the extended generalized gamma function |

Date |
Thu, 30 Aug 2012 18:01:50 +0100 |

Dear Statalist, I have sent this question before, but since it laked a considerable ammount of expressions and reference, I am sending the question again hoping for a possible anwser. This is the problem: I have a variable x, which is in logarithmic scale, that I want to adjust to the extended generalized gamma distribution following the approach used by R.L. Prentice 1974, "A log gamma model and its maximum likelihood Estimation", Biometrika, 61(3), pp 539-544 and developed by J.F. Lawless 1980, "Inference in the generalized gamma and log gamma distributions" Technometrics, 22(3) pp 409-419. in such a way I may replicate the work developed by Cabral & Mata 2003, "On the Evolution of the firm size distribution:Facts and Theory", The American Economic Review, 93(4), pp1075-1090. The first approach I considered was the streg command, which is not suitable for this problem, since there is a little change in the original expression of the extended generalized gamma function: starting from the original expression and considering the three parameters (mu, sigma, k). The parametrezation that I present considers the following transformation q = k^(-1/2), leading to the following expression (citing from Cabral and Mata 2003): if x follows an extended generalized gamma distribution, then w = (lnx - mu) / sigma has p.d.f. |q|*(q^-2)^(q^-2) *exp(q^(-2) *(qx - exp(qx))) / gamma(q^(-2)) if q is different from 0 (2pi)^(-1/2) èxp(-(1/2)x^(2)) if q is equal to 0 where gamma(t) is the gamma function. My objective is to estimate the three parameters (mu, sigma, q) and then to regress on x assuming that x follows an extended generalized gamma function (exactly the same as Cabral and Mata 2003 did) (Sorry for the messy expression...). I am using Stata 11.0. I am open to any suggestion and please correct me in case of mistakes. If any other information is needed, I will be please to add it to the question. Thanks for your consideration, Francisco Augusto * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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