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# Normal Distribution (Gaussian Distribution)

The Normal Distribution is the most important (but by no means the only) distribution for continuous values. Probability density:

```                                         2
1              1 |x - mu|
f(x) = ---------------- exp( - - |------| )
sqrt(2 pi) sigma        2 |sigma |
```

- loge f(x) :

```                                            2
1 |x - mu|
-ln f(x) = ln(sqrt(2 pi) sigma) + - |------|
2 |sigma |
```

This document is online at   http://www.csse.monash.edu.au/~lloyd/Archive/2005-05-Normal/index.shtml   and contains hyper-links to other resources.

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 Needs Sun Microsystems' Java ON! ©L.Allison  (au) mu= sigma= vertical: min= max=

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# Maximum Likelihood estimator

 muML = (x1 + x2 + . . . + xn) / n

 vML = SUMi=1..n (xi - muML)2/n

and sigma = sqrt(v).

Consider n=1, and n=2.

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# Minimum Message Length estimator

with prior h(mu,v) ~ 1/v

 muMML = (x1 + x2 + . . . + xn) / n = muML

 vMML = SUMi=1..n (xi - mu)2/(n-1)

and sigma = sqrt(v).

Consider n=1, and n=2.

© L. Allison, School of Computer Science and Software Engineering, Monash University, Australia 3800.
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