You can have two different formulas for the same thing.
Just like if you have a series of positive values, x1, x2, ... xn.
You can use the formula x1+x2+...+xn to compute the sum.
You can also use the formula exp(log(x1)*log(x2)*....*log(xn)) to compute the sum.
Mathematically they are equivalent.
Same thing with the CV formulas you referred to under the log-normal assumption.
I wrote the following program to show you how empirically you can get almost the same value between using these two formulas for CV --
data one; do sample=1 to 2000; call streaminit(2366); do i=1 to 2000; logx=rand('normal'); x=exp(logx); output; end; end; run;
proc means data=one noprint; by sample; var x logx; output out=out(drop=_freq_ _type_) mean(x)=meanx std(x)=stdx var(logx)=var_logx; run;
data out; set out; cv_x2 = sqrt(exp(var_logx)-1); cv_x = stdx/meanx; run;
proc means data=out mean; var cv_x cv_x2 ; run;
Hope this helps,
Jill
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