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QGDF: Quantifying Global Distribution Function (Machine Gnostics)

The QGDF class provides robust, assumption-free global quantification of data distributions using the Machine Gnostics framework. QGDF is designed for inlier-resistant, sample-wide analysis, making it ideal for heterogeneous, clustered, or uncertain datasets where dense regions may dominate.

Overview

QGDF is optimized for global quantification and density estimation, especially when data may contain dense clusters, inliers, 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.
  • Inlier-Resistant: Robust to dense clusters and inliers.
  • Flexible: Supports additive and multiplicative data forms.
  • Weighted Data: Incorporates sample weights for advanced analysis.
  • Automatic Parameter Estimation: Scale and bounds inferred from data.
  • Memory-Efficient: Optimized for large datasets.
  • Visualization: Built-in plotting for QGDF and PDF.
  • Customizable: Multiple solver options, bounds, and precision settings.

Key Features

  • Fits a global quantifying distribution function to your data
  • Robust to inliers and dense clusters
  • 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 QGDF, PDF, and bounds
  • Memory-efficient for large datasets
  • Detailed results and diagnostics

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)
z0_optimize bool True Optimize location parameter during fitting
tolerance float 1e-9 Convergence tolerance for optimization
data_form str 'a' Data form: 'a' (additive), 'm' (multiplicative)
n_points int 500 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 QGDF generation
flush bool True Flush large arrays (memory management)

Attributes

  • params: dictFitted parameters and results after fitting.
  • DLB, DUB, LB, UB, S, 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 QGDF to your data, estimating all relevant parameters and generating the global quantifying 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=False, extra_df=True, figsize=(12,8))

Visualizes the fitted QGDF and related plots.

  • plot_smooth: boolPlot smooth interpolated curve.
  • plot: str'qgdf', 'pdf', or 'both'.
  • bounds: boolShow bound lines.
  • extra_df: boolInclude 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 QGDF

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

# Initialize QGDF
qgdf = QGDF()

# Fit the model
qgdf.fit(data)

# Plot the results
qgdf.plot()

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

Notes

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

Author: Nirmal Parmar Date: 2025-09-24