diff --git a/pyeyesweb/analysis_primitives/statistical_moment.py b/pyeyesweb/analysis_primitives/statistical_moment.py
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+"""Statistical moments analysis module for signal processing.
+
+This module provides tools for computing various statistical moments from
+multivariate signal data. Statistical moments characterize the shape and
+properties of probability distributions and are fundamental in signal analysis.
+
+The available statistical moments include:
+1. Mean - Central tendency of the data
+2. Standard Deviation - Dispersion around the mean
+3. Skewness - Asymmetry of the distribution
+4. Kurtosis - Tailedness of the distribution
+
+Typical use cases include:
+1. Signal characterization and feature extraction
+2. Quality assessment of sensor data
+3. Motion pattern analysis in movement data
+4. Anomaly detection in time series data
+5. Distribution analysis in multivariate signals
+
+References
+----------
+1. Pearson, K. (1895). Contributions to the Mathematical Theory of Evolution.
+2. Fisher, R. A. (1925). Statistical Methods for Research Workers.
+"""
+
+import numpy as np
+from scipy import stats
+from pyeyesweb.data_models.sliding_window import SlidingWindow
+
+
+class StatisticalMoment:
+    """Real time statistical moments analyzer for signal data.
+
+    This class computes various statistical moments (mean, standard deviation,
+    skewness, kurtosis) from sliding window data to characterize signal
+    distributions and properties.
+    """
+
+    def __init__(self):
+        # No parameters in constructor as per comments
+        pass
+
+    def compute_statistics(self, signals: SlidingWindow, methods: list) -> dict:
+        """Compute statistical analysis for multivariate signals.
+
+        Parameters
+        ----------
+        signals : SlidingWindow
+            Sliding window buffer containing multivariate signal data.
+        methods : list of str
+            List of statistical methods to compute. Available options:
+            'mean', 'std_dev', 'skewness', 'kurtosis'
+
+        Returns
+        -------
+        dict
+            Dictionary containing statistical metrics.
+        """
+        if not signals.is_full():
+            return np.nan
+
+        data, _ = signals.to_array()
+        n_samples, n_features = data.shape
+
+        if n_samples < 2:
+            return np.nan
+
+        result = {}
+
+        # Compute only the requested statistical moments
+        for method in methods:
+            if method == 'mean':
+                values = np.mean(data, axis=0)
+                result['mean'] = float(values[0]) if len(values) == 1 else values.tolist()
+
+            elif method == 'std_dev':
+                values = np.std(data, axis=0, ddof=1)
+                result['std'] = float(values[0]) if len(values) == 1 else values.tolist()
+
+            elif method == 'skewness':
+                values = stats.skew(data, axis=0)
+                result['skewness'] = float(values[0]) if len(values) == 1 else values.tolist()
+
+            elif method == 'kurtosis':
+                values = stats.kurtosis(data, axis=0)
+                result['kurtosis'] = float(values[0]) if len(values) == 1 else values.tolist()
+
+            else:
+                # Skip invalid methods silently
+                continue
+
+        return result
+
+    def __call__(self, sliding_window: SlidingWindow, methods: list) -> dict:
+        """Compute statistical metrics.
+
+        Parameters
+        ----------
+        sliding_window : SlidingWindow
+            Buffer containing multivariate data to analyze.
+        methods : list of str
+            List of statistical methods to compute.
+
+        Returns
+        -------
+        dict
+            Dictionary containing statistical metrics.
+        """
+        return self.compute_statistics(sliding_window, methods)
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