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MathGroup Archive 2006

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Problem with the Sum Function -- Using a Benford Distribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66806] Problem with the Sum Function -- Using a Benford Distribution
  • From: Richard Palmer <mapsinc at bellatlantic.net>
  • Date: Wed, 31 May 2006 06:30:54 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

(* define a PDF*)
f = Log[10, 1 + 1/d]


(* compute for various values of the parameter *)
Table[Apply[Plus, Table[f, {d, 10 ^ h, 10 ^ (h + 1) - 1}]], {h, 0, 4}]// N


(* the mean is well defined *)
Table[ Apply[Plus, Table[d  Log[10, 1 + 1/d], {d, 10^h, 10^(h + 1) - 1}]]
//N, {h, 0, 4}] 

(* here is a parametric formula for the mean *)
mean =Assuming[k \[Element] Integers && k ? 0,    Sum[d Log[10, 1 + 1/d],
{d, 10^k, 10^(k + 1) - 1}]] // FullSimplify

(* the formula appears to be wrong *)
Table[N[mean], {k, 0, 4}]


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