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I have an application where I get back the time to perform an operation, the times are in the interval ]0:inf[ and I have this crazy idea. Lets say I know the mean of my dataset. woule it makes sense to test for normal distribution on the interval ]ln_n(0):mean[ if below mean and [mean:inf] above the mean, and if such a distribution existed to calculate std-dev's on it?

If this makes sense to anyone but me I'm sure someone has allready done it and could tell me what its called.

Martin Kristiansen
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  • I can't follow your idea. Do you want to test if the distribution of the proportion of your data less than the mean is normal via something like the Shapiro-Wilk test, & then again for the proportion above the mean? – gung - Reinstate Monica Dec 13 '13 at 00:18
  • @gung lets say I have some data [2ms, 4ms 12ms... ] it looks normally distributed I do however know that the data cannot data values below 0, how to I cramp my normal distribution into the interval from [0:inf]? Is the re a special kind of distribution for this? – Martin Kristiansen Dec 13 '13 at 00:29
  • There is probably no true normal distribution in the world (see [here](http://stats.stackexchange.com/questions/726//4301#4301)), nonetheless, the normal distribution is often a good enough approximation for many purposes. If your data are unimodal, tightly-clustered, w/ a mean far from 0, the normal might be OK. There are many dists that are used for durations, however, that might be a better fit. You could look at the [Weibull distribution](http://en.wikipedia.org/wiki/Weibull_distribution) or the [gamma distribution](http://en.wikipedia.org/wiki/Gamma_distribution), eg. – gung - Reinstate Monica Dec 13 '13 at 00:43
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    You description seems a little ambiguous (or maybe it's just my own confusion). Can you show an example, either a histogram (preferably with a good number of bins) or better, a normal Q-Qplot, which might give some better sense of what you're asking. Note that there are many continuous distribution on the positive half-line. – Glen_b Dec 13 '13 at 00:47

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