Gnostic Distribution Functions

Gnostic Distribution Functions (GDF) are a new class of probability and density estimators designed for robust, flexible, and assumption-free data analysis. Unlike traditional statistical distributions, GDFs do not require any prior assumptions about the underlying data distribution. Instead, they allow the data to "speak for themselves," making them especially powerful for small, noisy, or uncertain datasets.

More information available here.

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EGDF - Estimating Global Distribution Function

The EGDF provides a robust global estimate of the distribution function for your data.

Estimating Global Distribution Function

from machinegnostics.magcal import EGDF

# create an EGDF object
egdf = EGDF(verbose=False)

# fit the data
egdf.fit(data=data)

# plot GDF
egdf.plot(bounds=True)

# check parameters
print(egdf.params)

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ELDF - Estimating Local Distribution Function

The ELDF focuses on local properties of the data distribution, providing detailed insight into local data behavior.

Estimating Local Distribution Function

from machinegnostics.magcal import ELDF

# create an ELDF object
eldf = ELDF(verbose=False)

# fit the data
eldf.fit(data=data)

# plot GDF
eldf.plot(bounds=True)

# check parameters
print(eldf.params)

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QGDF - Quantifying Global Distribution Function

QGDF quantifies global distribution characteristics, useful for uncertainty quantification and diagnostics.

Quantifying Global Distribution Function

from machinegnostics.magcal import QGDF

# create a QGDF object
qgdf = QGDF(verbose=False)

# fit the data
qgdf.fit(data=data)

# plot GDF
qgdf.plot(bounds=True)

# check parameters
print(qgdf.params)

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QLDF - Quantifying Local Distribution Function

QLDF quantifies local distribution characteristics, providing fine-grained uncertainty and fidelity measures.

Quantifying Local Distribution Function

from machinegnostics.magcal import QLDF

# create a QLDF object
qldf = QLDF(verbose=False)

# fit the data
qldf.fit(data=data)

# plot GDF
qldf.plot(bounds=True)

# check parameters
print(qldf.params)

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Tips

• All GDF classes (EGDF, ELDF, QGDF, QLDF) follow a similar API: create an object, fit your data, plot results, and inspect parameters.
• Use the bounds=True option in .plot() to visualize uncertainty bounds.
• For more advanced usage and parameter tuning, see the API Reference.

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Next: Explore more tutorials and real-world examples in the Examples section!