375k views

### When (and why) should you take the log of a distribution (of numbers)?

Say I have some historical data e.g., past stock prices, airline ticket price fluctuations, past financial data of the company... Now someone (or some formula) comes along and says "let's take/use ...
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1k views

### Where does the logistic function come from?

I first learned the logistic function in machine learning, where it is just a function that map a real number to 0 to 1. We can use calculus to get the derivative and use it for some optimization ...
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18k views

### What is the most appropriate way to transform proportions when they are an independent variable?

I thought I understood this issue, but now I'm not as sure and I'd like to check with others before I proceed. I have two variables, X and ...
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8k views

### Why do we log transform response ratios?

In meta-analysis, it seems a standard practice to take the natural log of the response ratio before evaluating it. My question is why? That is, if I have a treatment mean (Xe) and a control mean of ...
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1k views

### How does logistic growth rate coincide with the slope of the line in the exponential phase of the growth?

For a logistic function $$f(x) = \frac{L}{1 + e^{-k(x - x_0)}},$$ people call $k$ the logistic growth rate. Now, I have encountered this statement: In the log scale the logistic growth rate coincides ...
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2k views

### What order preserving transformation makes data more evenly spread, decreasing the peak, and fattening the tails of the distribution?

How can I transform a variable (non linear transformation) such that its values are more evenly spread, that is reduce the peak in the middle of the histogram and move more into tails?
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