Back Transform of SHASH Transformed Value

[#1]

Hello,

I am trying to calculate normal tolerance intervals for a population of data which follows a non-normal distribution. After using SHASH transformation to transform the data to normal, can tolerance intervals be calculated and back-transformed to the native distribution? If so, is there a readily available formula or script by which to execute this back transformation?

If this is not possible, are there other suitable transformations for completing this type of analysis? In the past I have used a Johnson Su transformation for a similar purpose.

Any help would be greatly appreciated.

[#2]

Check out this earlier Community Discussion Back transform of Student t distribution transformation 

[#3]

Hi @scappuccio : Presumably, you used SHASHTrans(x, gamma, delta, theta, sigma), to transform to a normal distribution. Could you then use SHASHInv(z, gamma, delta, theta, sigma) to back-transform? Or am I missing something?