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my data ranges between x=(-10, 60). X represents energy savings after adopting an energy efficient product, where most individuals save energy (positive x) but a few use more energy (such as through the well-documented "rebound effect").

I think the phenomenon can be well modeled by an exponential distribution, mainly due to the long right tail of the exponential.

But I know that for the exponential, x>0. Should I try and shift the exponential distribution or choose another distribution (skewed normal)?

Blake Shurtz
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  • It would be good to know more about your problem. In principle, the answer is "yes" if you think a good model for the savings would consist of some non-negative quantity plus a random error: that can explain negative results. But you just don't provide enough information to let us know how to provide good advice. – whuber Dec 30 '18 at 16:33

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Suppose we shift all the X ∈ (–10, 60) values by adding 10. What happens if we observe –15 in future? No amount of shifting will ensure that we never get a negative value in future data.

If you just want to report how good the energy efficient product is, then I think a boxplot for X is good enough.

If you must estimate the distribution of X, then try kernel density estimation. But it takes a bit of trial and error to choose a good bandwidth.

farmer
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