Skip to content

DataIntervals: Robust Interval Estimation Engine (Machine Gnostics)

The DataIntervals class provides robust, adaptive, and diagnostic interval estimation for Gnostics Distribution Function (GDF) classes such as ELDF, EGDF, QLDF, and QGDF. It is designed to estimate meaningful data intervals (such as tolerance and typical intervals) based on the behavior of the GDF's central parameter (Z0) as the data is extended, while enforcing ordering constraints and providing detailed diagnostics.

Overview

DataIntervals is designed for advanced interval analysis in scientific, engineering, and reliability applications. It adaptively scans the data domain, extending the data with candidate values and tracking the variation of the central parameter Z0.

Key Features:

  • Adaptive Search: Efficiently scans the data domain with a dense search near the central value (Z0) and sparser search near the boundaries.
  • Robustness: Supports gnostic filtering (clustering) to enhance robustness against outliers.
  • Diagnostics: Provides warnings and errors for suboptimal settings and ordering violations.
  • Ordering Constraint: Ensures that the estimated intervals satisfy the natural ordering: ZL < Z0L < Z0 < Z0U < ZU.
  • Visualization: Plots Z0 variation, estimated intervals, and data coverage.

Parameters

Parameter Type Default Description
gdf ELDF/EGDF/QLDF/QGDF - Fitted GDF (Gnostics Distribution Function) object.
n_points int 10 Number of search points for interval estimation.
dense_zone_fraction float 0.4 Fraction of the search domain near Z0 to search densely.
dense_points_fraction float 0.7 Fraction of points allocated to the dense zone.
convergence_window int 15 Number of points in the moving window for convergence.
convergence_threshold float 1e-6 Threshold for standard deviation of Z0 in convergence window.
min_search_points int 30 Minimum number of search points before checking convergence.
boundary_margin_factor float 0.001 Margin factor to avoid searching exactly at the boundaries.
extrema_search_tolerance float 1e-6 Tolerance for detecting extrema in Z0 variation.
gnostic_filter bool False If True, apply gnostic clustering to filter outlier Z0 values.
catch bool True If True, catch and store warnings/errors internally.
verbose bool False If True, print detailed progress and diagnostics.
flush bool False If True, flush memory after fitting to save resources.

Attributes

  • ZL: float Lower bound of the typical data interval.
  • Z0L: float Lower bound of the tolerance interval (Z0-based).
  • Z0: float Central value (Z0) of the original GDF.
  • Z0U: float Upper bound of the tolerance interval (Z0-based).
  • ZU: float Upper bound of the typical data interval.
  • tolerance_interval: float Width of the tolerance interval (Z0U - Z0L).
  • typical_data_interval: float Width of the typical data interval (ZU - ZL).
  • ordering_valid: bool Whether the ordering constraint (ZL < Z0L < Z0 < Z0U < ZU) is satisfied.
  • params: dict Dictionary of parameters, warnings, errors, and results.
  • search_results: dict Raw search results for datum values and corresponding Z0s.

Methods

fit(plot=False)

Run the interval estimation process. Optionally plot results.

  • plot: bool (default=False). If True, automatically plot analysis results.

Returns: None

results()

Return a dictionary of estimated interval results and bounds.

Returns: Dict — A dictionary containing keys for LB, LSB, DLB, LCB, LSD, ZL, Z0L, Z0, Z0U, ZU, USD, UCB, DUB, USB, UB.

plot_intervals(figsize=(12, 8))

Plot the Z0 variation and estimated intervals.

  • figsize: tuple (default=(12, 8)).

Returns: None

plot(figsize=(12, 8))

Plot the GDF, PDF, and intervals on the data domain.

  • figsize: tuple (default=(12, 8)).

Returns: None

Example Usage

import numpy as np
from machinegnostics.magcal import ELDF, DataIntervals

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

# 1. Fit ELDF first
eld = ELDF()
eld.fit(data)

# 2. Run Interval Analysis
# create a DataIntervals object
data_intervals = DataIntervals(gdf=eldf)

# fit the data
data_intervals.fit()

# plot
data_intervals.plot()

# print intervals
data_intervals.results()

1770037703442

Notes

  • GDF Types: For best results, use with ELDF or QLDF.
  • Optimization: increasing n_points improves accuracy but increases computation time.
  • Usage: The class is designed for research and diagnostic use; adjust parameters for your data and application.

Author: Nirmal Parmar
Date: 2025-10-10