What is name of this distribution and can we have 68–95–99.7 rule for it?

I have a distribution like this:

• 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.

• 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. – Dan Aug 28 '14 at 18:50
• 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. – Glen_b Aug 28 '14 at 23:05

• 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? – user2991243 Aug 28 '14 at 21:27
• 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. – Dennis Aug 29 '14 at 5:50