I was introduced to the concept of quantile-based gaussian transform. To my understanding, it changes the value of the original data by each percentile to the matching percentile of gaussian distribution.
I have a few questions:
- What is the pros & cons of quantile transform vs power transform (ex: Box-Cox)
- Let say that you constructed the confidence interval of mean of lognormal distribution after transform. With power transformation, you can back transform the confidence interval by taking the inverse of the power raised. But how does it work in quantile transform? My professor said that you can backtransform the data, but I'm not sure how I can back transform the values of statistics obtained from the transformed data.
- Is there any case where quantile transform fail to obtain gaussian distribution?