pylevy

https://pylevy.readthedocs.io/en/latest/
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pylevy is a Python package for calculating Levy stable distributions (probability density function...
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### Get Parameters in a Specific Parametrization

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Instantiate a `Parameters` object and use the `get` method to retrieve the parameters in a desired parametrization. This is useful for converting parameters from within an existing `Parameters` object.

```python
>>> p = Parameters(par='1', alpha=1.5, beta=0.5, mu=0, sigma=1.2)  # to convert
>>> p.get('B')  # returns the parameters in the parametrization B
array([1.5       , 0.59033447, 0.03896531, 1.46969385])
```

--------------------------------

### Parameters Class and Conversion Utility

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Documentation for the Parameters class and its static method 'convert' for transforming Levy stable distribution parameters between different parametrizations.

```APIDOC
## Class Parameters

This class is a wrapper for the parameters of the Levy stable distribution. It facilitates fitting by allowing optimization on specific parameters. The primary utility function is `convert`, which transforms parameters between different available parametrizations.

### Class Method: convert

Use to convert a parameter array from one parametrization to another.

#### Parameters
- **pars** (ndarray) - Required - Array of parameters to be converted.
- **par_in** (str) - Required - Parametrization of the input array (e.g., '0', '1', 'A', 'B', 'M').
- **par_out** (str) - Required - Parametrization of the output array (e.g., '0', '1', 'A', 'B', 'M').

#### Returns
- **ndarray** - Array of parameters in the desired parametrization.

#### Examples
```python
import numpy as np
from pylevy import Parameters

a = np.array([1.6, 0.5, 0.3, 1.2])
b = Parameters.convert(a, '1', 'B')
print(b)
# Expected output: array([1.6       , 0.55457302, 0.2460079 , 1.4243171 ])

c = Parameters.convert(b, 'B', '1')
print(c)
# Expected output: array([1.6, 0.5, 0.3, 1.2])
np.testing.assert_allclose(a, c)
```

### Method: get

Same as `convert` but used from within a `Parameters` object instance.

#### Parameters
- **par_out** (str) - Optional - The desired output parametrization (e.g., '0', '1', 'A', 'B', 'M'). If None, returns parameters in the object's current parametrization.

#### Returns
- **ndarray** - Array of parameters in the specified or object's current parametrization.

#### Examples
```python
from pylevy import Parameters

p = Parameters(par='1', alpha=1.5, beta=0.5, mu=0, sigma=1.2)  # to convert
print(p.get('B'))
# Expected output: array([1.5       , 0.59033447, 0.03896531, 1.46969385])
```
```

--------------------------------

### Convert Parameters Between Parametrizations

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Use the `convert` class method to transform parameter arrays from one Levy stable distribution parametrization to another. Supported input and output parametrizations include '0', '1', 'A', 'B', and 'M'.

```python
>>> a = np.array([1.6, 0.5, 0.3, 1.2])
>>> b = Parameters.convert(a, '1', 'B')
>>> b
array([1.6       , 0.55457302, 0.2460079 , 1.4243171 ])
>>> c = Parameters.convert(b, 'B', '1')
>>> c
array([1.6, 0.5, 0.3, 1.2])
>>> np.testing.assert_allclose(a, c)
```

--------------------------------

### levy.Parameters Class

Source: https://pylevy.readthedocs.io/en/latest/genindex.html

This section details the methods available for the Parameters class within the levy module.

```APIDOC
## Class levy.Parameters

### Methods

- **convert()**
  - Description: Converts parameters.
  - Method: (Assumed to be a class method call, specific HTTP method not applicable)
  - Endpoint: (Not applicable for library methods)

- **get()**
  - Description: Gets parameters.
  - Method: (Assumed to be a method call, specific HTTP method not applicable)
  - Endpoint: (Not applicable for library methods)
```

--------------------------------

### Levy Module API

Source: https://pylevy.readthedocs.io/en/latest/_sources/levy.rst.txt

Documentation for the core classes and functions within the levy module.

```APIDOC
## levy.Parameters

### Description
Class representing the parameters for a Levy distribution.

## levy.random

### Description
Generates random numbers following a Levy distribution.

## levy.levy

### Description
Calculates values related to the Levy distribution.

## levy.fit_levy

### Description
Fits a Levy distribution to a given dataset.
```

--------------------------------

### Fit Levy Stable Distribution Parameters

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Estimates the parameters of a Levy stable distribution from data using Maximum Likelihood estimation. Allows fixing specific parameters to restrict the search.

```python
>>> np.random.seed(0)
>>> x = random(1.5, 0, 0, 1, shape=(200,))
>>> fit_levy(x) # -- Fit a stable distribution to x
(par=0, alpha=1.52, beta=-0.08, mu=0.05, sigma=0.99, 402.37150603509247)
```

```python
>>> fit_levy(x, beta=0.0) # -- Fit a symmetric stable distribution to x
(par=0, alpha=1.53, beta=0.00, mu=0.03, sigma=0.99, 402.43833088693725)
```

```python
>>> fit_levy(x, beta=0.0, mu=0.0) # -- Fit a symmetric distribution centered on zero to x
(par=0, alpha=1.53, beta=0.00, mu=0.00, sigma=0.99, 402.4736618823546)
```

```python
>>> fit_levy(x, alpha=1.0, beta=0.0) # -- Fit a Cauchy distribution to x
(par=0, alpha=1.00, beta=0.00, mu=0.10, sigma=0.90, 416.54249079255976)
```

--------------------------------

### Generate Random Alpha-Stable Variates

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Generates random values from an alpha-stable distribution using parametrization 0. Can also convert from other parametrizations.

```python
>>> rnd = random(1.5, 0, shape=(100,))  # parametrization 0 is implicit
>>> par = np.array([1.5, 0.905, 0.707, 1.414])
>>> rnd = random(*Parameters.convert(par ,'B' ,'0'), shape=(100,))  # example with convert
```

--------------------------------

### Calculate Levy Distribution PDF or CDF

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Computes the probability density function (PDF) or cumulative distribution function (CDF) for a Levy distribution. Uses parametrization 0 by default.

```python
>>> x = np.array([1, 2, 3])
>>> levy(x, 1.5, 0, cdf=True)
array([0.75634202, 0.89496045, 0.94840227])
```

--------------------------------

### levy Module Functions

Source: https://pylevy.readthedocs.io/en/latest/genindex.html

This section details the functions available within the levy module.

```APIDOC
## Module levy

### Functions

- **fit_levy()**
  - Description: Fits the Levy distribution.
  - Method: (Assumed to be a function call, specific HTTP method not applicable)
  - Endpoint: (Not applicable for library functions)

- **levy()**
  - Description: Generates Levy distribution samples.
  - Method: (Assumed to be a function call, specific HTTP method not applicable)
  - Endpoint: (Not applicable for library functions)

- **random()**
  - Description: Generates random Levy distribution samples.
  - Method: (Assumed to be a function call, specific HTTP method not applicable)
  - Endpoint: (Not applicable for library functions)
```

--------------------------------

### levy.levy

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Calculates the Levy distribution PDF or CDF with the tail replaced by an analytical power law approximation.

```APIDOC
## levy.levy

### Description
Computes the Levy distribution at specified values. Supports returning either the PDF or the CDF.

### Parameters
- **x** (ndarray) - Required - values where the function is evaluated
- **alpha** (float) - Required - alpha
- **beta** (float) - Required - beta
- **mu** (float) - Optional - mu (default: 0.0)
- **sigma** (float) - Optional - sigma (default: 1.0)
- **cdf** (bool) - Optional - specifies if it returns the cdf instead of the pdf (default: False)

### Response
- **ndarray** - Values of the pdf (or cdf) at x
```

--------------------------------

### levy.fit_levy

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Estimates parameters of a Levy stable distribution from data using Maximum Likelihood estimation.

```APIDOC
## levy.fit_levy

### Description
Estimate parameters of Levy stable distribution given data x, using Maximum Likelihood estimation. Allows restricting the search by fixing specific parameters.

### Parameters
- **x** (ndarray) - Required - values to be fitted
- **par** (str) - Optional - parametrization (default: '0')
- **kwargs** (dict) - Optional - additional parameters to fix during fitting

### Response
- **tuple** - A tuple containing a Parameters object and the negative log likelihood of the data.
```

--------------------------------

### levy.random

Source: https://pylevy.readthedocs.io/en/latest/levy.html

Generates random values sampled from an alpha-stable distribution using parametrization 0.

```APIDOC
## levy.random

### Description
Generate random values sampled from an alpha-stable distribution. This method is derived directly from the definition of a stable variable and uses parametrization 0.

### Parameters
- **alpha** (float) - Required - alpha
- **beta** (float) - Required - beta
- **mu** (float) - Optional - mu (default: 0.0)
- **sigma** (float) - Optional - sigma (default: 1.0)
- **shape** (tuple) - Optional - shape of the resulting array

### Response
- **ndarray** - Generated random values
```
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