I was reading about the relation between Kurtosis and Outliers on Wiki and got across a line 'An example of a platykurtic distribution is the uniform distribution, which does not produce outliers' https://en.wikipedia.org/wiki/Kurtosis
I mean it would also have some µ ± 2σ cut in probability density curve, then how can U.D not have outliers?
An uniform distribution has no outlier since the probability density function of the distribution is constant (i.e. all the possible values of all the possible intervals with equal length are equally likely).
Moreover, it can be shown that the possible values of an uniform distribution lies with in the interval
(mean - 3 x standard deviation , (mean + 3 x standard deviation)
implying that the distribution does not have outlier.
The link mentioned by Safa Aouinti will be helpful.
Thanks to her.
In a uniform distribution all outcomes between the minimum and the maximum are equally likely: there is no curve. If the underlying distribution is Uniform, one can get outliers if measurement error and mistakes are included. One can also get outliers through insufficient sampling; e.g. taking 7 samples from a Uniform(minimum=2,maximum=50) distribution. With so few observations my perception of the underlying distribution might be slightly off, or just wrong.
1) There is no central tendency of the data. The mean of a Uniform distribution is not the best guess as to the value of the next observation.
2) There are no outliers, no tails. If you calculate the standard deviation as you would for a Normal distribution, then the relationship that 68% of observations are within 1 standard deviation is not true. I have not thought about whether it is true if one uses the formula for the Uniform distribution to calculate standard deviation.
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