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From |
"Demetris Christodoulou" <D.Christodoulou@econ.usyd.edu.au> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Johnson SB distribution |

Date |
Thu, 20 Nov 2008 06:45:56 +1100 |

First of all, please accept my apologies for the previous null posting. My question revisits a previous posting dated 05 Dec 2003 when Nick Cox and Stephen Jenkins first advised me on a question related to the Johnson SB distribution (http://www.stata.com/statalist/archive/2003-12/msg00208.html). I was quite sure that there were more postings on this but I could not find them. A standardised Johnson SB is: > Y = (X - xi) / lambda and a unit normal Z can be represented as: > Z = gamma + delta * logit Y Therefore: > Y = invlogit((Z - gamma)/delta) > X = xi + lambda * invlogit((Z - gamma)/delta) In Stata terms, I could generate a Johnson SB by: . set obs 100000 . gen X_SB = xi + lambda * invlogit((invnorm(uniform()) - gamma)/delta) For instance, generate the X(xi, lambda, gamma, delta) = X(-1, 1, 3, 5): . gen X_SB = -1 + 2 * invlogit((invnorm(uniform()) - 3)/5) I expected that the variable X_SB would be distributed from -1 to 1, whereas the result is much narrower range. Is my logic wrong or is it something else? many thanks, Demetris * * 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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