1

I have the following equation, from http://www.mesasoftware.com/Papers/USING%20THE%20FISHER%20TRANSFORM.pdf

Screenshot of the relevant part

Because the parameters inside the log are (1+x)/(1-x), the output is always negative when x > 1.

But natural logarithms are only valid for positive number.

Anybody can explain that equation?

What am I missing?

Julien L
  • 111
  • 2
    Two possibilities: that x is restricted to being between -1 and 1; or that x is a complex number and you just have to pick a branch of the complex logarithm, which typically means that $\ln(-x) = \ln(x)+\pi i$ or similar. – Dan Uznanski Dec 29 '14 at 03:45
  • 1
    It's clearly restricted to $(-1,1)$, so that values close to $-1$ go off to $-\infty$ and those close to $1$ go off to $\infty$. That would produce a two-tailed distribution, but it's not going to look like a bell in the middle if the input distribution looks funny in the middle. – user21820 Dec 29 '14 at 04:28
  • 2
    The restriction $-1<x<1$ is stated in the first sentence on page 3 of the cited document. – David K Dec 29 '14 at 05:05
  • Thanks for your answers. I missed the range to which it was limited. – Julien L Jan 09 '15 at 15:54

0 Answers0