       Problem with the Sum Function -- Using a Benford Distribution

• To: mathgroup at smc.vnet.net
• Subject: [mg66838] Problem with the Sum Function -- Using a Benford Distribution
• From: Richard Palmer <mapsinc at bellatlantic.net>
• Date: Thu, 1 Jun 2006 06:54:37 -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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