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Date:         Tue, 29 Jun 1999 09:23:31 -0500
Reply-To:     Tim Dunsworth <Tim.Dunsworth@METROSTATE.EDU>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Tim Dunsworth <Tim.Dunsworth@METROSTATE.EDU>
Subject:      Re: Distribution method used to create random values
Comments: cc:
Content-Type: text/plain; charset=US-ASCII

Thanks for the confirmation, David. I would be curious to have a brief description and/or reference about the algorithm SPSS uses to directly generate normal random variates. The methods I have run across before all used one or more continuous variates and some brute force to get that result. They include: 1. compute the mean of a largish number of (0,1) variates, then rescale it. 2. treat the uniform variate roughly as a cumulative probability, then use an empirical polynomial approximation to the inverse CDF to get back to a z score. 3. generate pairs of uniform variates and then crank them through a hairy transform (which I don't recall off the top of my head) to get pairs of normal variates.

>>> "Nichols, David" <nichols@SPSS.COM> 06/28 2:49 PM >>> Yes, this is what's done for SAMPLE. Incidentally, all distributions other than the normal begin with the same uniform number generator algorithm, but a separate algorithm is used for direct production of normal pseudo-random numbers.

David Nichols Principal Support Statistician and Manager of Statistical Support SPSS Inc.

> -----Original Message----- > From: Tim Dunsworth [mailto:Tim.Dunsworth@METROSTATE.EDU] > Sent: Monday, June 28, 1999 10:44 AM > To: SPSSX-L@LISTSERV.UGA.EDU > Subject: Re: Distribution method used to create random values > > > The fundamental random number generator in SPSS is a uniform > number generator on the (0,1) interval, then various > rescalings or other manipulations are done to get any other > desired distribution. In this case, no further manipulation > is needed, since if you do, say, > SAMPLE .25 > then all SPSS has to do is generate a (0,1) uniform random > number for each observation and then select only those > observations with a value <.25. The manual version I have > does not say this in so many words, but it is implied by what > is said and I would be very surprised if the SPSS developers > did anything different than this simple approach. > > >>> <JonWoodlan@AOL.COM> 06/26 9:31 AM >>> > Hello folks, > > What distribution method (uniform, normal, etc.) does SPSS > 7.5.1 use to > create the random values in Data:Select Cases:Random Sample Of Cases? > > Thank you for your help. > > Jon Woodland > >

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