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

*To*: mathgroup at smc.vnet.net*Subject*: [mg50573] Re: [mg50544] Re: sorry, but more q's on random numbers*From*: DrBob <drbob at bigfoot.com>*Date*: Fri, 10 Sep 2004 04:06:43 -0400 (EDT)*References*: <200409090919.FAA19484@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

In line with Bill's answer, look in the ContinuousDistributions.m file which is in C:\Program Files\Wolfram Research\Mathematica\5.0\AddOns\StandardPackages\Statistics on my machine, and look for these lines: exponential = Compile[{{lambda, _Real}, {q, _Real}}, -Log[q]/lambda] ExponentialDistribution/: Random[ExponentialDistribution[lambda_:1]] := exponential[lambda, Random[]] As you can see, Mathematica computes Exponential variates by taking the Log of a Uniform variate. Bobby On Thu, 9 Sep 2004 05:19:13 -0400 (EDT), Bill Rowe <readnewsciv at earthlink.net> wrote: > On 9/8/04 at 5:15 AM, sean_incali at yahoo.com (sean kim) wrote: > >> What kind of distribution do I get if I take the base 10 Log of >> Random[Real, {range}]? > > A truncated reflected exponential distribution. For any distribution, the cumulative distribution function, cdf, maps the domain of the distribution to 0,1. In particular, the cdf for the exponential distribution is: > > << "Statistics`" > CDF[ExponentialDistribution[a], x] > > 1 - E^((-a)*x) > > Recognizing this must range from 0 to 1 and 1-Random[] is a uniform random deviate then > > Log[10, 1 - %] // PowerExpand > > -((a*x)/Log[10]) > > shows -Log[10,Random[]] to be a exponential distribution. Omitting the minus sign reflects the distribution about the origin. Adding a range restriction truncates the distribution. > >> is that Log Uniform? or normal? > > No, see above. > >> also What's the best way to show what type of distribution it is? >> I was thinking of listplot. > > There are a number of ways to show characteristics of the distribution. Which is best depends on what you are trying to show. Most of the time, I would plot some version of the empirical distribution function. For example, > > data = Sort@Table[Random[], {25}]; > ListPlot[Transpose@ > {data, > Rest@FoldList[Plus, 0, data]/Total@data}]; >However, often people perfer to see the density function which is approximated by plotting a histogram. The difficulty with plotting histograms is appropriately choosing the bin width. > -- > To reply via email subtract one hundred and four > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Re: sorry, but more q's on random numbers***From:*Bill Rowe <readnewsciv@earthlink.net>