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MathGroup Archive 2004

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50544] Re: sorry, but more q's on random numbers
  • From: Bill Rowe <readnewsciv at earthlink.net>
  • Date: Thu, 9 Sep 2004 05:19:13 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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.
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