One million times? Why? I really think that is overkill. I would try to cover more parameter combinations if it were me.

But you should be able to use a single data step to generate A-D statistics for all of your parameter combinations. The code below should be pretty efficient.

%macro AD(N=); do i=1 to &N; /* The next line needs completion with the appropriate G */ _x&N{i} = G(ranuni(6923479,S)); end;

call sortn(of _X&N(*)); mu = mean(of x1-x&N); var = var(of x1-x&N); sd = sqrt(var); S=0; do i=1 to &N; S + ((2*i - 1)/&N) * (log(cdf('normal',x{i},mu,sd)) + log(1 - cdf('normal',x{&N+1-i},mu,sd))); end; AD = -&N - S; output AD_&N; %mend;

/* Generate 10000 samples of same size (N=9 in this case) following */ /* a normal distribution and compute AD statistic for each sample. */ data AD_50 AD_100 AD_200 AD_300; array _x50 {50} x1-x50; array _x100 {100} x1-x100; array _x200 {200} x1-x200; array _X300 {300} x1-x300; do S={S1 S2 S3}; /* This line needs correct specification */ do rep=1 to 10000; %AD(N=50) %AD(N=100) %AD(N=200) %AD(N=300) end; end; keep S AD; run;

/* Determine probability of observed data */ /* using simulated data AD distribution. */ proc sort data=AD_50; by S AD; run;

proc sort data=AD_100; by S AD; run;

proc sort data=AD_200; by S AD; run;

proc sort data=AD_300; by S AD; run;

The above is untested code and should be tested with a small number of replicates before using it for a final simulation. Also, there will obviously need to be some final step where you determine the quantiles of the AD statistics.

Dale

--------------------------------------- Dale McLerran Fred Hutchinson Cancer Research Center mailto: dmclerra@NO_SPAMfhcrc.org Ph: (206) 667-2926 Fax: (206) 667-5977 ---------------------------------------

--- On Sun, 8/30/09, OR Stats <stats112@GMAIL.COM> wrote:

> From: OR Stats <stats112@GMAIL.COM> > Subject: Fastest Steps for Simulating: Anderson-Darling Goodness of Fit test for Non-typical distn > To: SAS-L@LISTSERV.UGA.EDU > Date: Sunday, August 30, 2009, 8:14 PM > This is good. I am ready now to run a large scale simulation. What that > means is that I want to compute the goodness of fit statistic for (M x > S) groups and n times each group. > > Group defined by (m,s); S = s1 s2 s3 and M = 50 100 200 300. Basically, > M is my different sample sizes for which I am testing their fit to > function G(random#,s) (i.e., inverse distribution). I would like to run > each group 1 million times. For each s group, by generating random > numbers just by 300 x 1million times, I'll have enough simulated data > y(s) to use for the largest and smaller sample sizes. > > My final column space would look like > i ranuni y_s1=G(ranuni,s1) y_s2=G(ranuni,s2) y_s3=G(ranuni,s3) > 1 > . > . > . > m > All rows in the above table would be used to caculate function f_s1, > f_s2, f_s3 (i.e., AD). This last step is repeated 1 Million times. > > Can we do this in one to two DATA STEPS? Which syntax would be fastest > since we have to generate 300 Million random numbers, from which we would > split the sample by 1 Million disjoint sets that we would then compute a > statistic 1 Million times using 50, 100, 200, and 300 rows of data at > each iteration for three different values of s (s1, s2, s3)? > > Thank Q!