I have a distribution like this:
What is name of this distribution?
As you know we have
normal distribution. Can we have something like this in this distribution?
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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.
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.