Re: sorry, but more q's on random numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg50537] Re: sorry, but more q's on random numbers*From*: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>*Date*: Thu, 9 Sep 2004 05:18:40 -0400 (EDT)*References*: <chmomi$a2a$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

The general rule for transforming probability density functions is Pr(x) = d(y)/d(x) Pr(y) where x and y are vector-valued, Pr(x) and Pr(y) are the PDFs expressed in x-space and y-space, and d(y)/d(x) is the Jacobian of the transformation. For your 1-dimensional problem this gives (assuming your range is a<=y<=b with a>0 to ensure you avoid the logarithmic singularity at y=0) P(y) = 1/(b-a), a<=y<=b (and Pr(y)=0 otherwise) x = log10(y) = ln(y)/ln(10) (using log10 to denote log base 10, and ln to denote natural log) y = exp(x log(10)) = 10^x d(y)/d(x) = 10^x ln(10) Pr(x) = 10^x ln(10)/(b-a), log10(a)<=x<=log10(b) (and Pr(x)=0 otherwise) Sanity check the result Integrate[10^x Log[10]/(b - a), {x, Log[10, a], Log[10, b]}] which gives 1 as required. You can plot this using (for example) With[{a=2,b=5}, Plot[10^x Log[10]/(b-a),{x,Log[10,a],Log[10,b]},PlotRange\[Rule]{0,Automatic}] ]; or if you want to show the probability surrounding the region where it is non-zero you can use (for example) f[x_,a_,b_]:=10^x Log[10]/(b-a)/;Log[10,a]\[LessEqual]x\[LessEqual]Log[10,b]; f[x_,a_,b_]:=0; With[{a=2,b=5}, Plot[f[x,a,b],{x,0,1},PlotRange\[Rule]{0,Automatic}] ]; Steve Luttrell "sean kim" <sean_incali at yahoo.com> wrote in message news:chmomi$a2a$1 at smc.vnet.net... > Hello Group, > > I hate to keep revisiting this, but if i may... > > What kind of distribution do I get if I take the base > 10 Log of Random[Real, {range}]? > > is that Log Uniform? or normal? > > Sorry for such newbie question. > > also What's the best way to show what type of > distribution it is? I was thinking of listplot. > > thanks in advance for any insights. > > sean > > > > __________________________________ > Do you Yahoo!? > Yahoo! Mail is new and improved - Check it out! > http://promotions.yahoo.com/new_mail >