Gaussian curve, x is a log scale

In summary, a Gaussian curve, also known as a normal distribution, is a symmetrical and bell-shaped statistical distribution that is often used to model natural phenomena. When plotted on a log scale, the curve appears to be more symmetrical and less skewed. This is because the log transformation compresses lower values and stretches higher values. On a log scale, the Gaussian curve will have a more pronounced peak and longer tails compared to a linear scale. Using a log scale for a Gaussian curve can help to better visualize and understand data, especially if there is a wide range of values. It is commonly used in fields such as finance, economics, and biology to model and analyze data, as well as in market research and risk management to understand consumer behavior
  • #1
nobahar
497
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.
 
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  • #2
The Gaussian curve is
[tex]y= ae^{-x^2}[/tex]
so if x is a log scale you have
[tex]y= ae^{-(log x)^2}[/itex]
No, that is not a linear function.
 
  • #3
Thanks Halls.
 

1. What is a Gaussian curve?

A Gaussian curve, also known as a normal distribution, is a statistical distribution that is symmetrical and bell-shaped. It is often used to model natural phenomena and is characterized by its mean and standard deviation.

2. How is the Gaussian curve related to a log scale?

A log scale is a nonlinear scale in which the values are plotted on a logarithmic axis rather than a linear one. When a Gaussian curve is plotted on a log scale, the curve appears to be more symmetrical and less skewed than when plotted on a linear scale.

3. What are the properties of a Gaussian curve on a log scale?

On a log scale, the Gaussian curve will have a more pronounced peak and longer tails compared to a linear scale. This is because the log transformation compresses the lower values and stretches the higher values, resulting in a more symmetrical curve.

4. What is the significance of using a log scale for a Gaussian curve?

Using a log scale for a Gaussian curve can help to better visualize and understand the data, especially if the data has a wide range of values. It can also help to identify patterns and trends that may not be visible on a linear scale.

5. What are some real-world applications of a Gaussian curve on a log scale?

The Gaussian curve on a log scale is often used in fields such as finance, economics, and biology to model and analyze data. It is also commonly used in market research and risk management to understand consumer behavior and make predictions about future trends.

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