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I have a distribution like this:

enter image description here

  • What is name of this distribution?

  • As you know we have 68–95–99.7 rule in normal distribution. Can we have something like this in this distribution?

Thanks.

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    $\begingroup$ There is no easy answer to this question. There are a multitude of distributions that will resemble the above distribution. For example, the exponential distribution will look like that or a beta distribution with the right parameters. $\endgroup$ – Dan Aug 28 '14 at 18:50
  • $\begingroup$ The numbers 68, 95 and 99.7 apply because those are the proportions within 1, 2 and 3 sds of the mean for the normal distribution (note that they don't really apply - except in quite large samples from normal distributions - when you estimate the mean and sd). A new distribution means different numbers. If you're dealing with a skewed distribution like that - even if you knew which one you had - it doesn't necessarily make so much sense to quantify the proportions within 1, 2 and 3 sds of the mean. For example, with the exponential distribution, there's nothing more than 1sd below the mean. $\endgroup$ – Glen_b Aug 28 '14 at 23:05
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Perhaps it is a Exponential distribution with parameter 10, or a Gamma(1,8) distribution, or a Beta(0.5,2) distribution, or a ..... Hopefully the point is clear.

enter image description here

Of course once the distribution is chosen you can work backwards to figure out what values of the SD's will give you the 68-95-99.7 rule you want although how useful is that rule for an arbitrary distribution is debatable.

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  • $\begingroup$ Dan, I have another question. As you know exponential distribution has a tail. my data range for x-axes is from 0 to 1. I don't want this tail in exponential distribution after 1. Is any other revised other distribution for that? $\endgroup$ – user2991243 Aug 28 '14 at 21:27
  • $\begingroup$ The beta distribution lives between 0 to 1. $\endgroup$ – Dan Aug 28 '14 at 21:51
  • $\begingroup$ In the case of a heavily skewed distribution like this the whole idea of such a rule is silly. Moving to the left any fraction of $\sigma$ brings in more of the distribution than moving the same distance to the right. By the way, that is true whether we are starting at $\mu$, or anyplace else at least that distance above the lower bound on the support. $\endgroup$ – Dennis Aug 29 '14 at 5:50

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