DataframeKurtosis / Aggregation Layer

Calculate kurtosis (measure of tail heaviness) across specified columns, similar to scipy.stats.kurtosis or pandas kurtosis().

Mathematical form: $K = \frac{\sum _{i = 1}^{n} ( x _{i} - x ˉ ) ^{4} / n}{s ^{4}}$ Where:

$\overset{x}{ˉ}$ is the mean
$s$ is the standard deviation
$n$ is the number of observations

Interpretation:

High kurtosis: Heavy tails, more outliers
Low kurtosis: Light tails, fewer outliers
Normal distribution: 3.0 (Pearson) or 0.0 (Fisher)

Common applications:

Financial risk analysis
Quality control in manufacturing
Outlier detection systems
Signal processing
Environmental data analysis
Behavioral studies

Provides multiple configuration options for detailed statistical analysis.

Table

Select

[column, ...]

Numeric columns to compute kurtosis for. If empty, processes all numeric columns. Non-numeric columns are ignored. Selected columns should contain sufficient non-null values for meaningful kurtosis calculation.

Kurtosis

[, ...]

Configuration for kurtosis calculation, allowing choice between Fisher's and Pearson's definitions and bias correction options.

Fisher

bool

true

Definition selection for kurtosis calculation:

true (default): Fisher's definition (normal = 0.0)
false: Pearson's definition (normal = 3.0)

Fisher's is often preferred in modern statistics for its normalized scale.

Bias

bool

true

Controls bias correction in calculation:

true (default): Use biased moment estimators
false: Apply bias correction

Bias correction important for small samples but increases variance.