A quantile estimator derived from a normally distributed population with unknown mean and standard deviation.
A normal theory quantile is most powerful when a random sample is from a population with a normal distribution.
In many cases, the data are skewed to the right and do not follow a normal distribution. A Box-Cox (or logarithmic) transform can correct the skewness, allowing you to use the Normal theory quantile. If not, a distribution-free estimator may be more powerful (IFCC, 1987).
