Advanced Probability Distributions for AI and Statistics
Project description
Advanced Distributions
Advanced probability distributions for:
- AI Research
- Machine Learning
- Heavy-tail Modeling
- Diffusion Models
- Statistical Research
- Copula Theory
- Quantum Probability
- Information Theory
Install
pip install advanced_distributions
# # =============================================================
# # EXAMPLE USAGE: slash distribution
# # =============================================================
# if __name__ == "__main__":
# dist = SlashDistribution(
# mu=0,
# sigma=1
# )
# print("Mean:", dist.mean())
# print(
# "Variance:",
# dist.var()
# )
# print(
# "Standard Deviation:",
# dist.std()
# )
# print(
# "Skewness:",
# dist.skewness()
# )
# print(
# "Kurtosis:",
# dist.kurtosis()
# )
# print(
# "Entropy:",
# dist.entropy()
# )
# print(
# "Median:",
# dist.median()
# )
# print(
# "Mode:",
# dist.mode()
# )
# print(
# "Moment(2):",
# dist.moment(2)
# )
# print(
# "\nPDF at x=1:",
# dist.pdf(1)
# )
# print(
# "CDF at x=1:",
# dist.cdf(
# np.array([1])
# )[0]
# )
# print(
# "Hazard at x=1:",
# dist.hazard(1)
# )
# print(
# "MGF at t=0.01:",
# dist.mgf(0.01)
# )
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate samples
# samples = dist.rvs(
# size=5000
# )
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = (
# SlashDistribution.fit(
# samples
# )
# )
# print("\nFitted Parameters:")
# print("mu =", fitted.mu)
# print("sigma =", fitted.sigma)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
# # =============================================================
# # EXAMPLE USAGE: Fractal distribution
# # =============================================================
# if __name__ == "__main__":
# dist = FractalDistribution(
# D=1.3,
# lambda_=0.8
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("\n3rd Moment:", dist.moment(3))
# print("\nPDF at x=2:", dist.pdf(2))
# print("CDF at x=2:", dist.cdf(np.array([2]))[0])
# print("Hazard at x=2:", dist.hazard(np.array([2]))[0])
# # Generate Samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted_params = FractalDistribution.fit(samples)
# print("\nFitted Parameters:")
# print("D =", fitted_params[0])
# print("lambda =", fitted_params[1])
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# # =============================================================
# # EXAMPLE USAGE: Fractional distribution
# # =============================================================
# if __name__ == "__main__":
# dist = FractionalDistribution(
# alpha=1.7,
# beta=2.0,
# gamma=0.9
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("3rd Moment:", dist.moment(3))
# print("\nPDF at x=2:", dist.pdf(2))
# print("CDF at x=2:", dist.cdf(np.array([2]))[0])
# print("Hazard at x=2:", dist.hazard(np.array([2]))[0])
# print("MGF at t=0.1:", dist.mgf(0.1))
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted_params = FractionalDistribution.fit(samples)
# print("\nFitted Parameters:")
# print("alpha =", fitted_params[0])
# print("beta =", fitted_params[1])
# print("gamma =", fitted_params[2])
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
# # =============================================================
# # EXAMPLE USAGE: GeneralizedParetoDistribution
# # =============================================================
# if __name__ == "__main__":
# dist = GeneralizedParetoDistribution(
# xi=0.3,
# sigma=2.0,
# mu=0.0
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("3rd Moment:", dist.moment(3))
# print("\nPDF at x=2:", dist.pdf(2))
# print("CDF at x=2:", dist.cdf(2))
# print("Hazard at x=2:", dist.hazard(2))
# print("MGF at t=0.1:", dist.mgf(0.1))
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate random samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = GeneralizedParetoDistribution.fit(samples)
# print("\nFitted Parameters:")
# print("xi =", fitted.xi)
# print("sigma =", fitted.sigma)
# print("mu =", fitted.mu)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
# # =============================================================
# # EXAMPLE USAGE: HyperbolicSecantDistribution
# # =============================================================
# if __name__ == "__main__":
# dist = HyperbolicSecantDistribution(
# mu=0,
# sigma=1
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("3rd Moment:", dist.moment(3))
# print("\nPDF at x=1:", dist.pdf(1))
# print("CDF at x=1:", dist.cdf(1))
# print("Hazard at x=1:", dist.hazard(1))
# print("MGF at t=0.2:", dist.mgf(0.2))
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = HyperbolicSecantDistribution.fit(samples)
# print("\nFitted Parameters:")
# print("mu =", fitted.mu)
# print("sigma =", fitted.sigma)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
# # # =============================================================
# # EXAMPLE USAGE: LevyStableDistribution
# # =============================================================
# if __name__ == "__main__":
# dist = LevyStableDistribution(
# alpha=1.7,
# beta=0.2,
# loc=0,
# scale=1
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("Moment(0.5):", dist.moment(0.5))
# print("\nPDF at x=1:", dist.pdf(1))
# print("CDF at x=1:", dist.cdf(1))
# print("Hazard at x=1:", dist.hazard(1))
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate random samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = LevyStableDistribution.fit(samples)
# print("\nFitted Parameters:")
# print("alpha =", fitted.alpha)
# print("beta =", fitted.beta)
# print("loc =", fitted.loc)
# print("scale =", fitted.scale)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
# # =============================================================
# # EXAMPLE USAGE:NeuralSplineDistribution
# # =============================================================
# if __name__ == "__main__":
# dist = NeuralSplineDistribution()
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("Moment(3):", dist.moment(3))
# print("\nPDF at x=1:", dist.pdf(1))
# print("CDF at x=1:", dist.cdf(np.array([1]))[0])
# print("Hazard at x=1:",
# dist.hazard(np.array([1]))[0])
# print("MGF at t=0.1:",
# dist.mgf(0.1))
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = NeuralSplineDistribution.fit(samples)
# print("\nFitted Knot Positions:")
# print("knots_x =", fitted.knots_x)
# print("knots_y =", fitted.knots_y)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
# # =============================================================
# # EXAMPLE USAGE: QuantileDistribution
# # =============================================================
# if __name__ == "__main__":
# dist = QuantileDistribution(
# mu=0,
# sigma=1,
# alpha=1.5,
# beta=2.0
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("Moment(3):", dist.moment(3))
# print("\nPDF at x=1:",
# dist.pdf(np.array([1]))[0])
# print("CDF at x=1:",
# dist.cdf(np.array([1]))[0])
# print("Hazard at x=1:",
# dist.hazard(np.array([1]))[0])
# print("MGF at t=0.1:",
# dist.mgf(0.1))
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate random samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = QuantileDistribution.fit(samples)
# print("\nFitted Parameters:")
# print("mu =", fitted.mu)
# print("sigma =", fitted.sigma)
# print("alpha =", fitted.alpha)
# print("beta =", fitted.beta)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
# # =============================================================
# # EXAMPLE USAGE: QuantumProbabilityDistribution
# # =============================================================
# if __name__ == "__main__":
# dist = QuantumProbabilityDistribution(
# sigma=1.0,
# k=2.0,
# mu=0.0
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("Moment(4):", dist.moment(4))
# print(
# "Energy Expectation:",
# dist.energy_expectation()
# )
# print("\nPDF at x=1:",
# dist.pdf(1))
# print("CDF at x=1:",
# dist.cdf(np.array([1]))[0])
# print("Hazard at x=1:",
# dist.hazard(np.array([1]))[0])
# print("MGF at t=0.1:",
# dist.mgf(0.1))
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate random samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = QuantumProbabilityDistribution.fit(
# samples
# )
# print("\nFitted Parameters:")
# print("mu =", fitted.mu)
# print("sigma =", fitted.sigma)
# print("k =", fitted.k)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_wave_function()
# dist.plot_histogram()
# # =============================================================
# # EXAMPLE USAGE: csinhDistribution
# # =============================================================
# if __name__ == "__main__":
# dist = SinhArcsinhDistribution(
# epsilon=1.0,
# delta=0.8,
# mu=0,
# sigma=1
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print("Standard Deviation:", dist.std())
# print("Skewness:", dist.skewness())
# print("Kurtosis:", dist.kurtosis())
# print("Entropy:", dist.entropy())
# print("Median:", dist.median())
# print("Mode:", dist.mode())
# print("Moment(4):", dist.moment(4))
# print("\nPDF at x=1:",
# dist.pdf(1))
# print("CDF at x=1:",
# dist.cdf(1))
# print("Hazard at x=1:",
# dist.hazard(1))
# print("MGF at t=0.1:",
# dist.mgf(0.1))
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate random samples
# samples = dist.rvs(size=5000)
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = SinhArcsinhDistribution.fit(
# samples
# )
# print("\nFitted Parameters:")
# print("epsilon =", fitted.epsilon)
# print("delta =", fitted.delta)
# print("mu =", fitted.mu)
# print("sigma =", fitted.sigma)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
# # =============================================================
# # EXAMPLE USAGE: SkewedStudentTDistribution
# # =============================================================
# if __name__ == "__main__":
# dist = SkewedStudentTDistribution(
# nu=8,
# lam=0.3,
# mu=0,
# sigma=1
# )
# print("Mean:", dist.mean())
# print("Variance:", dist.var())
# print(
# "Standard Deviation:",
# dist.std()
# )
# print(
# "Skewness:",
# dist.skewness()
# )
# print(
# "Kurtosis:",
# dist.kurtosis()
# )
# print(
# "Entropy:",
# dist.entropy()
# )
# print(
# "Median:",
# dist.median()
# )
# print(
# "Mode:",
# dist.mode()
# )
# print(
# "Moment(4):",
# dist.moment(4)
# )
# print(
# "\nPDF at x=1:",
# dist.pdf(1)
# )
# print(
# "CDF at x=1:",
# dist.cdf(
# np.array([1])
# )[0]
# )
# print(
# "Hazard at x=1:",
# dist.hazard(1)
# )
# print(
# "MGF at t=0.1:",
# dist.mgf(0.1)
# )
# print(
# "Characteristic Function at t=1:",
# dist.characteristic_function(1)
# )
# # Generate random samples
# samples = dist.rvs(
# size=5000
# )
# print("\nRandom Samples:")
# print(samples[:10])
# # Fit distribution
# fitted = (
# SkewedStudentTDistribution.fit(
# samples
# )
# )
# print("\nFitted Parameters:")
# print("nu =", fitted.nu)
# print("lam =", fitted.lam)
# print("mu =", fitted.mu)
# print("sigma =", fitted.sigma)
# # Plotting
# dist.plot_pdf()
# dist.plot_cdf()
# dist.plot_histogram()
Release history Release notifications | RSS feed
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
Built Distribution
Filter files by name, interpreter, ABI, and platform.
If you're not sure about the file name format, learn more about wheel file names.
Copy a direct link to the current filters
File details
Details for the file advanced_distributions-0.1.2.tar.gz.
File metadata
- Download URL: advanced_distributions-0.1.2.tar.gz
- Upload date:
- Size: 16.4 kB
- Tags: Source
- Uploaded using Trusted Publishing? No
- Uploaded via: twine/6.2.0 CPython/3.13.9
File hashes
| Algorithm | Hash digest | |
|---|---|---|
| SHA256 |
461f014c8c3d43694dcbfbdacb9a3bf3df69c4633c10543585e3f10a728213fc
|
|
| MD5 |
c59a47775981ed7c15fb4dc140bb4544
|
|
| BLAKE2b-256 |
ccdd23048ff1cf7def5febc89fdeca5275ba0a9527d6d9726172091b82494f3b
|
File details
Details for the file advanced_distributions-0.1.2-py3-none-any.whl.
File metadata
- Download URL: advanced_distributions-0.1.2-py3-none-any.whl
- Upload date:
- Size: 31.1 kB
- Tags: Python 3
- Uploaded using Trusted Publishing? No
- Uploaded via: twine/6.2.0 CPython/3.13.9
File hashes
| Algorithm | Hash digest | |
|---|---|---|
| SHA256 |
65221ec207d5bf7dc4fe621c8674b48901084ad21ad2fb8d7992bfb99c4c999a
|
|
| MD5 |
d0c3f5358c632d7f9560b8a888310d44
|
|
| BLAKE2b-256 |
29737318699ab72cf227019a2b8523ff760a2a692b561a94bfc33e319eede8af
|
