Gaussian curve, x is a log scale

Click For Summary
SUMMARY

The discussion centers on the behavior of the Gaussian function, specifically when the x-axis is represented on a logarithmic scale. The Gaussian function is defined as y = ae^{-x^2}. When x is transformed to a logarithmic scale, the equation becomes y = ae^{-(log x)^2}. It is concluded that this transformation does not yield a linear function, countering the initial assumption that it would appear linear at first glance.

PREREQUISITES
  • Understanding of Gaussian functions and their properties
  • Familiarity with logarithmic scales and transformations
  • Basic knowledge of mathematical notation and functions
  • Experience with graphing functions and interpreting their behavior
NEXT STEPS
  • Explore the properties of Gaussian functions in depth
  • Learn about logarithmic transformations and their effects on function shapes
  • Study the implications of non-linear transformations in data analysis
  • Investigate mathematical representations of functions in different scales
USEFUL FOR

Mathematicians, data scientists, and anyone interested in the behavior of functions under different scaling transformations.

nobahar
Messages
482
Reaction score
2
Hello!
If I have the gaussian function, but x is a loarithmic scale. Can I infer that, if x was plotted using a regualr scale, that the function would be 'fairly' linear? At least initially? As the rate of change gradually increases befor slowing down again. I think this is reasonable... I don't know how to try and represent it mathematically.
 
Physics news on Phys.org
The Gaussian curve is
y= ae^{-x^2}
so if x is a log scale you have
y= ae^{-(log x)^2}[/itex]<br /> No, that is not a linear function.
 
Thanks Halls.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 15 ·
Replies
15
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 22 ·
Replies
22
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K