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From |
"Eric G. Wruck" <ewruck@econalytics.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Generating random variables with logistic distribution |

Date |
Thu, 4 Aug 2005 11:29:32 -0400 |

This rang a bell so I went back to Mood, Graybill & Boes (1974). What you are interested in is called a probability integral transform (p. 202 if you have that book). "...Conversely, if U is uniformly distributed over the interval (0,1), then X = F-1(U) has cumulative distribution function Fx()." Unfortunately, I can't seem to do sub- & superscripts here in Eudora, but the F-1() is supposed to be the inverse cumulative distribution function for the random variable X. So if you have the cdf for the logistic, you should be able to generate an rv L that is distributed according to the logistic distribution. As an example, I took the simple logistic case with parameters alpha = 0 & beta = 1. Here's what I get with a sample of 1,000: . gen u = uniform() . gen L = -ln((1 - u)/u) . summ L, de L ------------------------------------------------------------- Percentiles Smallest 1% -4.747468 -7.249973 5% -3.048538 -6.471672 10% -2.17264 -5.892376 Obs 1000 25% -1.153445 -5.352503 Sum of Wgt. 1000 50% .0949801 Mean -.0038691 Largest Std. Dev. 1.805678 75% 1.139236 5.268712 90% 2.159457 5.512243 Variance 3.260474 95% 2.882929 5.750656 Skewness -.1215126 99% 4.709992 6.240138 Kurtosis 3.704852 . The theoretical mean is alpha, or zero in this case, so it looks somewhat close. The theoretical variance is (beta times pi) squared divided by 3, or approximately 3.299, so again close. Hope this helps. Eric >I know how to generate random variables with normal and uniform distributions. How about other distributions - in particular, logistic? Is there a program around that already does this, or can somebody tell me what the formula is? I seem to vaguely remember seeing something like this but now I can't find it. Thanks. > > >------------------------------------------- >Richard Williams, Notre Dame Dept of Sociology >OFFICE: (574)631-6668, (574)631-6463 >FAX: (574)288-4373 >HOME: (574)289-5227 >EMAIL: Richard.A.Williams.5@ND.Edu >WWW (personal): http://www.nd.edu/~rwilliam >WWW (department): http://www.nd.edu/~soc > >* >* For searches and help try: >* http://www.stata.com/support/faqs/res/findit.html >* http://www.stata.com/support/statalist/faq >* http://www.ats.ucla.edu/stat/stata/ -- =================================================== Eric G. Wruck Econalytics 2535 Sherwood Road Columbus, OH 43209 ph: 614.231.5034 cell: 614.330.8846 eFax: 614.573.6639 eMail: ewruck@econalytics.com website: http://www.econalytics.com ==================================================== * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Generating random variables with logistic distribution***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

**References**:**st: Generating random variables with logistic distribution***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

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