Implementation:Online ml River Stats Kurtosis

Knowledge Sources	Online_ml_River
Domains	Online_Learning, Statistics
Last Updated	2026-02-08 16:00 GMT

Overview

Kurtosis computes the running kurtosis of a data stream using Welford's algorithm.

Description

This statistic measures the "tailedness" of a distribution - whether data tends to have heavy or light tails compared to a normal distribution. It calculates the fourth standardized moment incrementally. The implementation uses Rust for performance and supports both biased and unbiased estimators through the bias parameter. Positive kurtosis indicates heavy tails with more outliers, while negative kurtosis indicates light tails.

Usage

Use Kurtosis when you need to understand the tail behavior of streaming data distributions. This is useful in risk assessment, quality control, anomaly detection, and financial analysis where understanding the likelihood of extreme values is important. It helps identify distributions with more or fewer outliers than expected.

Code Reference

Source Location

• Repository: Online_ml_River
• File: river/stats/kurtosis.py

Signature

class Kurtosis(stats.base.Univariate):
    def __init__(self, bias=False):
        super().__init__()
        self.bias = bias
        self._kurtosis = _rust_stats.RsKurtosis(bias)

Import

from river import stats

I/O Contract

Inputs

Name	Type	Required	Description
x	numbers.Number	Yes	Value to update the statistic with
bias	bool	Yes (init)	If False, calculations are corrected for statistical bias (default: False)

Outputs

Name	Type	Description
get()	float	Current kurtosis value (excess kurtosis, 0 for normal distribution)

Usage Examples

from river import stats
import numpy as np

np.random.seed(42)
X = np.random.normal(loc=0, scale=1, size=10)

# Unbiased kurtosis
kurtosis = stats.Kurtosis(bias=False)
for x in X:
    kurtosis.update(x)
    print(f"Kurtosis: {kurtosis.get():.4f}")

# Output (final values):
# -3.0
# -2.0
# -1.5
# 1.4130
# 0.1537
# 0.4614
# -1.6206
# -1.3540
# -1.2310
# -0.9490

# Biased kurtosis
kurtosis_biased = stats.Kurtosis(bias=True)
for x in X:
    kurtosis_biased.update(x)
    print(f"Biased Kurtosis: {kurtosis_biased.get():.4f}")

# Detecting heavy-tailed distributions
heavy_tail = stats.Kurtosis()
# Add data with outliers
for x in [1, 2, 3, 4, 5, 100]:  # 100 is an outlier
    heavy_tail.update(x)

print(f"Kurtosis with outlier: {heavy_tail.get():.4f}")
# Positive value indicates heavy tails

Related Pages

• Environment:Online_ml_River_Python_Runtime_Environment