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Assuming that I have a one-dimensional data set with a known distribution (i.e. normal, gamma, Weibull, etc.), is there a R function that I can call on the data set that will return the anomalies?

I know that anomaly detection in a known normally distributed data set is pretty straightforward but I couldn't even find a R functions for this, let alone some of the more complicated distributions.

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    $\begingroup$ Why not just compute thresholds with the quantile functions? $\endgroup$ – Julián Urbano Jul 5 '13 at 16:16
  • $\begingroup$ See here to start with. There is an outlier package in R. Did you go through that? $\endgroup$ – Metrics Jul 5 '13 at 16:25
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Although no doubt functions exist that may be helpful, this is just to underline that what you want is more difficult to do definitively than you imply.

Even for the case of a normal (Gaussian) distribution as reference distribution

  • If a data set is known to be normally distributed, there can't be anomalies.

  • If it is thought to be normally distributed except for the anomalies, telling the two apart requires estimation of the mean and standard deviation of the normal component, or something that is equivalent. There are numerous ways to do that, which means that the problem is very open-ended.

The other examples you give (gamma, Weibull) are loosely speaking more difficult still.

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