I'm computing Normal Tolerance Intervals and sometimes need to transform the data first. I typical try SHASH and Johnson SL. My question regards SHASH: What does it mean when the SHASH Distribution doesn't fit but the resulting transformed data are Normal? Conversely, what does it mean when SHASH fits but the resulting transformed data are not Normal? I am following the guidelines from a standards organization governing my work which allow for a monotonic transformation to Normality so I think that since the first case results in a Normal outcome, I should be able to use SHASH. although I am uncomfortable with not having a good fit. For the second case but I am curious about what it means for SHASH to fit when the result is not Normal. Thanks.
Hi @jayg001 : So I can fully understand of your question(s) and respond appropriately, can you tell me if I'm understanding your two situations.
Given a column of data, X:
1." What does it mean when the SHASH Distribution doesn't fit but the resulting transformed data are Normal?"
So, on this case, X does not have a SHASH distribution and you are applying some transformation (I'll call this function SHASH) to X to get a second column Y. So, Y = SHASH[X]. Further, Y appears to be normally distributed. Do I have this correct? What function (I've called SHASH[X]) are you using to transform X? I am familiar with the SHASH distribution, but I'm just looking for clarity here.
2. "Conversely, what does it mean when SHASH fits but the resulting transformed data are not Normal?"
In this case, X has a SHASH distribution. Then, a applying the SHASH transform (as in 1 above), you have Y = SHASH[X]. And further, Y does not appear to have a normal distribution.
Do I have this correct?
