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You could use

  2/pi*arctan(X/n)

for any n > 1; the larger n, the less steep the function.

An even simpler function is

  x/(x+n)

Michael

> Date: Thu, 26 Apr 2012 14:28:20 -0400
> From: Dan Abner <[log in to unmask]>
> Subject: Transformation from (0,+inf) to (0,1) XXXX
>
> Hi everyone,
>
> I have a variable (X) with only a lower bound (0) and need to map it
> to the (0,1) interval. Can anyone make suggestions on the best way to
> do this?
>
> I was considering:
>
> 2/pi*arctan(X)
>
> but this function is VERY steep and does not utlize most of the (0,1) space.
>
> Suggestions?
>
> Thanks!
>
> Dan

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