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ELDF: Estimating Local Distribution Function (Machine Gnostics)

The ELDF class provides robust, assumption-free local distribution estimation for real-world data using the Machine Gnostics framework. ELDF is designed for detailed local analysis, peak detection, and modal characterization, making it ideal for noisy, uncertain, or heterogeneous datasets.

Overview

ELDF is optimized for local probability and density estimation, especially when data may contain outliers, inner noise, or unknown distributions. It leverages gnostic algebra and error geometry to deliver resilient, interpretable results without requiring prior statistical assumptions.

  • Assumption-Free: No parametric forms or distributional assumptions.
  • Robust: Handles outliers, inner noise, and contaminated data.
  • Flexible: Supports additive and multiplicative data forms.
  • Weighted Data: Incorporates sample weights for advanced analysis.
  • Automatic Parameter Estimation: Scale and bounds inferred from data.
  • Advanced Z0 Estimation: Finds the gnostic mean (location of maximum PDF).
  • Memory-Efficient: Optimized for large datasets.
  • Visualization: Built-in plotting for ELDF and PDF.
  • Customizable: Multiple solver options, bounds, and precision settings.

Key Features

  • Fits a local distribution function to your data
  • Robust to outliers and inner noise
  • Supports weighted and unweighted samples
  • Automatic or manual bounds and scale selection
  • Additive ('a') and multiplicative ('m') data forms
  • Advanced optimization with customizable tolerance and solver
  • Visualization of ELDF, PDF, and bounds
  • Memory-efficient for large datasets
  • Detailed results and diagnostics
  • Variable scale parameter option for heteroscedasticity

Parameters

Parameter Type Default Description
DLB float or None None Data Lower Bound (absolute minimum, optional)
DUB float or None None Data Upper Bound (absolute maximum, optional)
LB float or None None Lower Probable Bound (practical lower limit, optional)
UB float or None None Upper Probable Bound (practical upper limit, optional)
S float or 'auto' 'auto' Scale parameter (auto-estimated or fixed value)
varS bool False Use variable scale parameter during optimization
z0_optimize bool True Optimize location parameter Z0 during fitting
tolerance float 1e-9 Convergence tolerance for optimization
data_form str 'a' Data form: 'a' (additive), 'm' (multiplicative)
n_points int 1000 Number of points for distribution curve
homogeneous bool True Assume data homogeneity
catch bool True Store intermediate results (memory usage)
weights np.ndarray or None None Prior weights for data points
wedf bool False Use Weighted Empirical Distribution Function
opt_method str 'L-BFGS-B' Optimization method (scipy.optimize)
verbose bool False Print progress and diagnostics
max_data_size int 1000 Max data size for smooth ELDF generation
flush bool True Flush large arrays (memory management)

Attributes

  • params: dict
    Fitted parameters and results after fitting.
  • DLB, DUB, LB, UB, S, varS, z0_optimize, tolerance, data_form, n_points, homogeneous, catch, weights, wedf, opt_method, verbose, max_data_size, flush:
    Configuration parameters as set at initialization.

Methods

fit(data, plot=False)

Fits the ELDF to your data, estimating all relevant parameters and generating the local distribution function.

  • data: np.ndarray, shape (n_samples,)
    Input data array.
  • plot: bool (optional)
    If True, automatically plots the fitted distribution.

Returns:
None (results stored in params)

plot(plot_smooth=True, plot='both', bounds=True, extra_df=True, figsize=(12,8))

Visualizes the fitted ELDF and related plots.

  • plot_smooth: bool
    Plot smooth interpolated curve.
  • plot: str
    'eldf', 'pdf', or 'both'.
  • bounds: bool
    Show bound lines.
  • extra_df: bool
    Include additional distribution functions.
  • figsize: tuple
    Figure size.

Returns:
None (displays plot)

results()

Returns a dictionary of all fitted parameters and results.

Returns:
dict (fitted parameters, bounds, scale, diagnostics, etc.)

Example Usage

import numpy as np
from machinegnostics.magcal import ELDF

# Example data
data = np.array([ -13.5, 0, 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])

# Initialize ELDF
eldf = ELDF()

# Fit the model
eldf.fit(data)

# Plot the results
eldf.plot()

# Access fitted parameters
results = eldf.results()
print("Local scale parameter:", results['S_opt'])
print("Distribution bounds:", results['LB'], results['UB'])

Notes

  • ELDF is robust to outliers and suitable for non-Gaussian, contaminated, or uncertain data.
  • Supports both additive and multiplicative data forms.
  • Use weights for advanced analysis (e.g., clustering, risk).
  • For large datasets, set catch=False to save memory.
  • Visualization options allow in-depth analysis of local distribution structure.
  • For more information, see GDF documentation and Machine Gnostics.

Author: Nirmal Parmar
Date: 2025-09-24