The Gaussian Distribution Is Inevitable (and This Beautiful Principle Proves It)

Comments (1)

kqr · 9h ago

> the only honest choice when all you know is mean and variance

This is said as if it were a realistic set of assumptions.

You almost always know more than that. Frequently you have at least a few samples from the distribution. Often you don't know the mean and variance with any certainty. The mean is relatively easily estimated with a fair number of samples, but variance is rather tricky to estimate with any precision.

Some processes don't even have a variance (or have infinite variance, depending on how you like to phrase it) but any set of samples from them will definitely have a variance. Are you going to shoehorn the normal distribution onto that process? I hope not.

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The Gaussian Distribution Is Inevitable (and This Beautiful Principle Proves It)

Comments (1)