Date: Tue, 4 Jun 2002 16:58:30 -0700 Cassell.David@EPAMAIL.EPA.GOV "SAS(r) Discussion" "David L. Cassell" Re: lapalcian [sic] distribution Vs Gaussian pdf text/plain; charset=us-ascii

Hristo Stevic <hristostev@YAHOO.COM> wrote [in part]: > about the percentage values which show what percentage of data will be > in a certain range of the pdf standard deviation, for example in > gaussian distribution > 68% of the observations fall within 1 standard deviation of the mean. > > want to know if there are similar reported percentage when using > laplacian distribution

You can see for yourself. SAS now has the CDF() function, which will let you get any 'percentage' that you want for a whole list of distributions, including the Laplace (or double exponential) function. Use it like this:

P = cdf('LAPLACE',x,theta,lambda);

where x is the point for which you want P(X <= x), theta is the optional location parameter, and lambda is the optional scale parameter.

The mean of the Laplace distribution is equal to theta, and the variance is equal to 2*lambda**2 . [So 1 standard deviation is lambda * sqrt(2).]

You will find if you do the math that the probability of being within 1 s.d. of the mean of a Laplace distribution is about 0.7568833 , regardless of the values of theta and lambda. Here's a trivial SAS check on that:

data temp; do lambda = 1 to 5; x = lambda*sqrt(2); P = cdf('LAPLACE',x,0,lambda) - cdf('LAPLACE',-x,0,lambda); put lambda= P= ; end; run;

lambda=1 P=0.7568832656 lambda=2 P=0.7568832656 lambda=3 P=0.7568832656 lambda=4 P=0.7568832656 lambda=5 P=0.7568832656

HTH, David -- David Cassell, CSC Cassell.David@epa.gov Senior computing specialist mathematical statistician

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