Date:         Wed, 24 Aug 2005 22:48:33 -0700
Reply-To:     David L Cassell <davidlcassell@MSN.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         David L Cassell <davidlcassell@MSN.COM>
Subject:      Re: Question: Underlying distributions in monte carlo simulation.
In-Reply-To:  <MC10-F41msYAvveRbIs001c18bc@mc10-f4.hotmail.com>
Content-Type: text/plain; format=flowed

phlarsen@YAHOO.COM wrote:
>I'm currently running this command in SAS:
>
>%let NumofDraws=10000;
>
>DATA DRAWS (keep = FIPS DRAW_P_STD--LN_DRAW_CDD I);
>  set WXDATA;
>  DO I=1 TO &NumofDraws.;
>  ****NORMAL DRAWS*****;
>  Draw_P_STD=P_STD_Mean+sqrt(P_STD_Vari)*rannor(0); *****Zero pegs seed at
>time of day.  See SAS notes on RANNOR fcn.;
>
>         *****LOGNORMAL DRAWS*****;
>         LN_Draw_P_STD=exp(P_STD_Mean+sqrt(P_STD_Vari)*rannor(0));
>         OUTPUT;
>         END;
>run;
>
>My question is this: Is there a way to plug in the skew and kurtosis into a
>random draw command (i.e. similar to rannor, but obviously better able to
>change the distribution's shape from normal).  Previous posts point to
>reading in a PDF input dataset (i.e. bins with percentages) and using that
>for the underlying distribution for the draw.  Any thoughts/ideas are
>greatly appreciated.

Working from an artificially-constructed pdf or cdf seems like a reasonable
alternative.

Here are a couple more suggestions you might try.

[1] Consider starting with a 3-parameter or 4-parameter generalized gamma
distribution.  You may be able to find formulae for the first four moments
and back-calculate to appropriate values of the parameters before doing
the sampling.

[2] Consider using a mixture distribution.  If you start with a mixture of
k normal distributions (where k is something simple, like 2 or 3) and you
weight
the mixture, then you can try to control the skewness and kurtosis of the
mixture distribution.

HTH,
David
--
David L. Cassell
mathematical statistician
Design Pathways
3115 NW Norwood Pl.
Corvallis OR 97330

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