Your team is building a predictive-maintenance model for turbine engines. The continuous feature fuel_flow_rate (kg/s) is strongly right-skewed, and about 3 % of the observations are exactly 0 kg/s when the engine is idle. To stabilize variance and approximate normality you decide to call scipy.stats.boxcox so the optimal Box-Cox power λ can be estimated. Which preparatory step is required before invoking the function so that the transformation and its likelihood calculation are well-defined for every observation?
Subtract the sample mean to center the data around zero before applying Box-Cox.
Standardize the feature to zero mean and unit variance; this alone makes Box-Cox valid.
Mark the idle (0 kg/s) rows as missing or drop them, and apply Box-Cox to the remaining records unchanged.
Add the same small positive constant to every value so the entire feature becomes strictly greater than 0, then run Box-Cox.
Box-Cox is mathematically defined only for strictly positive inputs. Both the power term y^λ (when λ ≠ 0) and the special logarithmic case (λ = 0) break down at y ≤ 0. Therefore every observation must be shifted above zero by adding the same small positive constant (for example, 1 × 10⁻⁶ or 1 on the native scale). Centering, standardizing, or dropping the zero rows does not guarantee strictly positive inputs, and scipy.stats.boxcox will raise an error if any value is non-positive. Shifting preserves the relative ordering of observations and allows λ to be estimated on valid data, after which the inverse shift can be applied to return predictions to the original scale.
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Why is the Box-Cox transformation only defined for strictly positive values?
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How do you choose an appropriate small constant to make data strictly positive for Box-Cox?
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What happens if you ignore this preparatory step and apply Box-Cox directly to non-positive values?