# Questions tagged [normal-distribution]

The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is one of the most important distributions in statistics. Use the [normality] tag for asking about testing for normality.

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### How is it possible to compare powers of normality tests?

The famous paper  compares the power of several normality tests. Regardless of its result, my immediate question is, "How is that even possible?" Well, the definition of power in this ...
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### Comparing groups that are impacted to different extent by same truncation

Say I have results for a running event, where there is a cutoff time that is the same for all participants. I assume the results are normally or log-normally distributed, but truncated at the cutoff ...
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### Combining factors, represented as normal distributions, to one combined factor, normally distributed

I'm trying to combine the different factors that may affect running pace, such as GPS-measured distance, grade, terrain, heat and other factors (such as wind etc.). Each factor is represented as a ...
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### Will this converge to origin?

Suppose you have a diffusion of 100 points with the following iteration: $$(x_{n+1},y_{n+1}) \sim \mathcal{N}\left((x_n,y_n), \frac{x_n^2 + y_n^2}{2} I_{2 \times2}\right)$$ This will make a high ...
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### Variance of powers of a standard normal random variable

To predict growth of money in a stock market I try to calculate expected return over a longer timeframe (e.g. 30 years) with a confidence interval. The simple math of taking an average stock market ...
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