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From |
Austin Nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Estimating the parameters of the GB2 distribution with incomplete knowledge of sample statistics |

Date |
Sun, 26 Sep 2010 22:25:57 -0400 |

Julio Estevez <je_123@hotmail.com>: -gbgfit- on SSC will give the MLE based only on the quantiles; you can write the MLE incorporating knowledge of the mean. Or you can use -nl- or Mata's optimize() of which there are examples in the archives. On Sun, Sep 26, 2010 at 4:32 PM, Julio Estevez <je_123@hotmail.com> wrote: > Hi > I am interested in deducing the parameters of a GB2 distribution given that I know just a couple of quantiles and sample statistics of the population I am interested in. > > I know the mean of the population of interest. I also know some key quantiles from the left side of the distribution. That is I know x1, x2, x3 such that F(x1) = 0.1, F(x2) = 0.2, F(x3) = 0.3 been F() the c.d.f. Although I do not know much about the upper tail, from previous research I beleive that the GB2 distribution may be good approximation of the distribution I am looking at. > > I beleive I can use the fact that GB2 distribution has distribution function (c.d.f.) F(x) = ibeta(p, q, (x/b)^a/(1+(x/b)^a) ) to estimate the parameters of the distribution function (a,b,p,q) given my knowledge about the mean and the first qualtiles. Then I can explore the upper tail under the assumption that my data is distributed as a GB2 > > Can somebody help me to set up the program to estimate these parameters? I believe it is "just" a matter of solving a set of 4 nonlinear equations with 4 unknowns, but my programming skills are not that good. > > The four equations will look like > mean = b*G(p+1/a)*G(q-1/a)/[G(p)G(q)]F(x1) = 0.1 = ibeta(p, q, (x1/b)^a/(1+(x1/b)^a)F(x2) = 0.2 = ibeta(p, q, (x2/b)^a/(1+(x2/b)^a)F(x3) = 0.3 = ibeta(p, q, (x3/b)^a/(1+(x3/b)^a) > from which the unknowns, a,b, p and q can be retrieved. > with G(.) been the gamma function > > Any help will be greatly appreciated! > Thanks > > Julio > > * * * 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/

**References**:**st: Estimating the parameters of the GB2 distribution with incomplete knowledge of sample statistics***From:*Julio Estevez <je_123@hotmail.com>

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