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Pre-Transforming Data
To aid in fitting a distribution, it is often helpful to pre-transform data that has physical bounds. Pre-transforming data takes data that is bounded and converts it to unbounded data. Bounds, if they exist, can be specified along with the data in the Data window.
When a lower bound (LB) is specified, the data can be pre-transformed using the transformation:
This transforms the range from LB to infinity to -infinity to infinity. A value equal to LB cannot be transformed by this equation. Such a value is replaced with LB + Precision/4 before performing the pre-transform. Take as example were the values are reported to the nearest 0.1 units (precision) and the lower bound is zero. Then the values correspond to:
Value Interval Midpoint
0 [0, 0.05] 0.025
0.1 [0.05, 0.15] 0.1
0.2 [0.15, 0.25] 0.2
0.3 [0.25, 0.35] 0.3
This is why 0.025 = precision/4 is used in place of zero when performing the pre-transform.
When an upper bound (UB) is specified, the data can be pre-transformed using the transformation:
This transforms the range from -infinity to UB to -infinity to infinity. A value equal to UB cannot be transformed by this equation. Such a value is replaced with UB - Precision/4 before performing the pre-transform.
When both a lower bound (LB) and upper bound (UB) are specified, the data can be pre-transformed using the transformation:
This transforms the range from LB to UB to -infinity to infinity. A value equal to LB cannot be transformed by this equation. Such a value is replaced with LB + Precision/4 before performing the pre-transform. A value also equal to UB cannot be transformed by this equation. Such a value is replaced with UB - Precision/4 before performing the pre-transform.