554: Transformation Settings
The Transform Y Data option attempts to transform the data to a normal distribution before performing the calculations. It proceeds by converting the original data to percentiles and then converts the percentiles to standard normal distribution deviates. Then, when calculations are complete, the results are transformed back to the original data distribution, again by means of percentiles. The original data distribution can be presented in one of two ways:
- Using the empirical distribution : for transformation to normal, the data are converted to percentiles based on their ranks; for transformation back to the empirical distribution, the percentiles are linearly interpolated onto the original data (if the percentile lies beyond the range of the original data, then a linear interpolation is applied based on the difference between the most extreme and the second most extreme values).
- Using a fitted gamma distribution : whose parameters are estimated using Thom's (1958) Monthly Weather Review algorithm . The gamma distribution is used by default if the SPI standardisation is selected.
Note that the transformation may not be effective if there are a number of ties in the original data.