Powerlaw

https://pythonhosted.org/powerlaw/
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Powerlaw is a Python package for analyzing and fitting power law distributions to empirical data...
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### GET /cdf

Source: https://pythonhosted.org/powerlaw/index.html

Returns the cumulative distribution function (CDF) of the data.

```APIDOC
## GET /cdf

### Description
Returns the cumulative distribution function of the data.

### Parameters
#### Query Parameters
- **original_data** (bool) - Optional - Whether to use all of the data initially passed to the Fit object.
- **survival** (bool) - Optional - Whether to return the survival function (1-CDF).

### Response
#### Success Response (200)
- **X** (array) - The sorted, unique values in the data.
- **probabilities** (array) - The portion of the data that is less than or equal to X.
```

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

### GET /ccdf

Source: https://pythonhosted.org/powerlaw/index.html

Returns the complementary cumulative distribution function (CCDF) of the data.

```APIDOC
## GET /ccdf

### Description
Returns the complementary cumulative distribution function of the data.

### Parameters
#### Query Parameters
- **original_data** (bool) - Optional - Whether to use all of the data initially passed to the Fit object.
- **survival** (bool) - Optional - Whether to return the CCDF or the CDF.

### Response
#### Success Response (200)
- **X** (array) - The sorted, unique values in the data.
- **probabilities** (array) - The portion of the data that is greater than or equal to X.
```

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

### Initial Parameters

Source: https://pythonhosted.org/powerlaw/index.html

Retrieves or calculates initial parameters for the distribution.

```APIDOC
## Get Initial Parameters

### Description
Returns previously user-provided initial parameters or, if never provided, calculates new ones. Default initial parameter estimates are unique to each theoretical distribution.

### Method
`initial_parameters`

### Parameters
#### Parameters
- **data_** (list or array) - The data to use for calculating initial parameters if not provided by the user.

### Returns
- **tuple or list** - Initial parameter values.
```

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

### POST /distribution_compare

Source: https://pythonhosted.org/powerlaw/index.html

Compares two distribution fits using the loglikelihood ratio.

```APIDOC
## POST /distribution_compare

### Description
Returns the loglikelihood ratio, and its p-value, between the two distribution fits.

### Parameters
#### Request Body
- **dist1** (string) - Required - Name of the first candidate distribution.
- **dist2** (string) - Required - Name of the second candidate distribution.
- **nested** (bool) - Optional - Whether the candidate distributions are nested.
```

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

### find_xmin

Source: https://pythonhosted.org/powerlaw/index.html

Finds the optimal xmin beyond which the scaling regime of the power law fits best by minimizing the Kolmogorov-Smirnov distance.

```APIDOC
## find_xmin

### Description
Returns the optimal xmin beyond which the scaling regime of the power law fits best. The attribute self.xmin of the Fit object is also set.

### Parameters
#### Query Parameters
- **xmin_distance** (None) - Optional - Distance parameter for optimization.
```

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

### bisect_map

Source: https://pythonhosted.org/powerlaw/index.html

Uses binary search to find the target solution to a function.

```APIDOC
## bisect_map

### Description
Uses binary search to find the target solution to a function, searching in a given ordered sequence of integer values.

### Parameters
#### Request Body
- **mn** (numeric) - Required - Minimum range value.
- **mx** (numeric) - Required - Maximum range value.
- **function** (function) - Required - A function that takes a single integer input.
- **target** (numeric) - Required - The target value of the function.
```

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

### PDF Calculation

Source: https://pythonhosted.org/powerlaw/index.html

Calculates the Probability Density Function (PDF) for the power law distribution.

```APIDOC
## Calculate PDF

### Description
Returns the probability density function (normalized histogram) of the theoretical distribution for the values in data within xmin and xmax, if present.

### Method
`pdf`

### Parameters
#### Parameters
- **data** (list or array, optional) - If not provided, attempts to use the data from the Fit object in which the Distribution object is contained.

### Returns
- **probabilities** (array) - The probability density function values.
```

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

### Plot PDF

Source: https://pythonhosted.org/powerlaw/index.html

Plots the Probability Density Function (PDF) of the theoretical distribution.

```APIDOC
## Plot PDF

### Description
Plots the probability density function (PDF) of the theoretical distribution for the values given in data within xmin and xmax, if present. Plots to a new figure or to axis ax if provided.

### Method
`plot_pdf`

### Parameters
#### Parameters
- **data** (list or array, optional) - If not provided, attempts to use the data from the Fit object in which the Distribution object is contained.
- **ax** (matplotlib axis, optional) - The axis to which to plot. If None, a new figure is created.

### Returns
- **ax** (matplotlib axis) - The axis to which the plot was made.
```

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

### nested_distribution_compare

Source: https://pythonhosted.org/powerlaw/index.html

Compares two distribution fits assuming they are nested versions of each other.

```APIDOC
## nested_distribution_compare

### Description
Returns the loglikelihood ratio, and its p-value, between the two distribution fits, assuming the candidate distributions are nested.

### Parameters
#### Request Body
- **dist1** (string) - Required - Name of the first candidate distribution (ex. ‘power_law’)
- **dist2** (string) - Required - Name of the second candidate distribution (ex. ‘exponential’)
- **nested** (bool) - Optional - Whether to assume the candidate distributions are nested versions of each other. True by default.

### Response
#### Success Response (200)
- **R** (float) - Loglikelihood ratio of the two distributions’ fit to the data.
- **p** (float) - Significance of R
```

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

### pdf

Source: https://pythonhosted.org/powerlaw/index.html

Returns the probability density function (normalized histogram) of the data.

```APIDOC
## pdf

### Description
Returns the probability density function (normalized histogram) of the data.

### Parameters
#### Request Body
- **original_data** (bool) - Optional - Whether to use all of the data initially passed to the Fit object.

### Response
#### Success Response (200)
- **bin_edges** (array) - The edges of the bins of the probability density function.
- **probabilities** (array) - The portion of the data that is within the bin.
```

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

### Parameter Range Check

Source: https://pythonhosted.org/powerlaw/index.html

Checks if the current parameters of the distribution are within the valid range.

```APIDOC
## Check Parameter Range

### Description
Checks whether the current parameters of the distribution are within the range of valid parameters.

### Method
`in_range`

### Returns
- **bool** - True if parameters are in range, False otherwise.
```

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

### Method: KS

Source: https://pythonhosted.org/powerlaw/index.html

Returns the Kolmogorov-Smirnov distance D between the distribution and the data.

```APIDOC
## Method KS

### Description
Returns the Kolmogorov-Smirnov distance D between the distribution and the data. Also sets the properties D+, D-, V (the Kuiper testing statistic), and Kappa.

### Parameters
- **data** (list or array) - Optional - If not provided, attempts to use the data from the Fit object.
```

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

### CDF and CCDF Calculation

Source: https://pythonhosted.org/powerlaw/index.html

Calculate the Cumulative Distribution Function (CDF) or Complementary Cumulative Distribution Function (CCDF) for the power law distribution.

```APIDOC
## CDF Calculation

### Description
Calculates the cumulative distribution function (CDF) of the theoretical distribution. Can be calculated for the values given in data within xmin and xmax, if present.

### Method
`cdf`

### Parameters
#### Parameters
- **data** (list or array, optional) - If not provided, attempts to use the data from the Fit object in which the Distribution object is contained.
- **survival** (bool, optional) - Whether to calculate a CDF (False) or CCDF (True). False by default.

### Returns
- **X** (array) - The sorted, unique values in the data.
- **probabilities** (array) - The portion of the data that is less than or equal to X.

## CCDF Calculation

### Description
Calculates the complementary cumulative distribution function (CCDF) of the theoretical distribution. Can be calculated for the values given in data within xmin and xmax, if present.

### Method
`cdf`

### Parameters
#### Parameters
- **data** (list or array, optional) - If not provided, attempts to use the data from the Fit object in which the Distribution object is contained.
- **survival** (bool, optional) - Whether to calculate a CDF (False) or CCDF (True). True by default.

### Returns
- **X** (array) - The sorted, unique values in the data.
- **probabilities** (array) - The portion of the data that is less than or equal to X.
```

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

### Fit Distribution

Source: https://pythonhosted.org/powerlaw/index.html

Fits the parameters of the distribution to the provided data using specified options.

```APIDOC
## Fit Distribution

### Description
Fits the parameters of the distribution to the data. Uses options set at initialization.

### Method
`fit`

### Parameters
#### Parameters
- **data** (list or array, optional) - If not provided, attempts to use the data from the Fit object in which the Distribution object is contained.
- **suppress_output** (bool, optional) - Suppresses output during fitting.
```

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

### Set Parameter Range

Source: https://pythonhosted.org/powerlaw/index.html

Sets the limits for parameter ranges during fitting.

```APIDOC
## Set Parameter Range

### Description
Sets the limits on the range of valid parameters to be considered while fitting.

### Method
`parameter_range`

### Parameters
#### Parameters
- **r** (dict) - A dictionary of the parameter range. Restricted parameter names are keys, and with tuples of the form (lower_bound, upper_bound) as values.
- **initial_parameters** (tuple or list, optional) - Initial parameter values to start the fitting search from.

### Returns
- **None**
```

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

### Generate Random Numbers

Source: https://pythonhosted.org/powerlaw/index.html

Generates random numbers from the theoretical power law distribution.

```APIDOC
## Generate Random Numbers

### Description
Generates random numbers from the theoretical probability distribution. If xmax is present, it is currently ignored.

### Method
`generate_random`

### Parameters
#### Parameters
- **n** (int or float) - The number of random numbers to generate.
- **estimate_discrete** (boolean, optional) - For discrete distributions, whether to use a faster approximation of the random number generator. If None, attempts to inherit the estimate_discrete behavior used for fitting from the Distribution object or the parent Fit object, if present. Approximations only exist for some distributions (namely the power law). If an approximation does not exist an estimate_discrete setting of True will not be inherited.

### Returns
- **r** (array) - Random numbers drawn from the distribution.
```

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

### Method: ccdf

Source: https://pythonhosted.org/powerlaw/index.html

Calculates the complementary cumulative distribution function (CCDF) of the theoretical distribution.

```APIDOC
## Method ccdf

### Description
The complementary cumulative distribution function (CCDF) of the theoretical distribution. Calculated for the values given in data within xmin and xmax, if present.

### Parameters
- **data** (list or array) - Optional - If not provided, attempts to use the data from the Fit object.
- **survival** (bool) - Optional - Whether to return the survival function.
```

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

### Likelihoods Calculation

Source: https://pythonhosted.org/powerlaw/index.html

Calculates the likelihoods of the observed data from the theoretical distribution.

```APIDOC
## Calculate Likelihoods

### Description
Calculates the likelihoods of the observed data from the theoretical distribution. Another name for the probabilities or probability density function.

### Method
`likelihoods`

### Parameters
#### Parameters
- **data_** (list or array) - The data for which to calculate likelihoods.

### Returns
- **array** - The likelihoods of the data.
```

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

### Log Likelihoods Calculation

Source: https://pythonhosted.org/powerlaw/index.html

Calculates the logarithm of the likelihoods of the observed data.

```APIDOC
## Calculate Log Likelihoods

### Description
Calculates the logarithm of the likelihoods of the observed data from the theoretical distribution.

### Method
`loglikelihoods`

### Parameters
#### Parameters
- **data_** (list or array) - The data for which to calculate log likelihoods.

### Returns
- **array** - The log likelihoods of the data.
```

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

### powerlaw.loglikelihood_ratio

Source: https://pythonhosted.org/powerlaw/index.html

Calculates a loglikelihood ratio and the p-value for testing which of two probability distributions is more likely to have created a set of observations.

```APIDOC
## powerlaw.loglikelihood_ratio

### Description
Calculates a loglikelihood ratio and the p-value for testing which of two probability distributions is more likely to have created a set of observations.

### Method
POST (assumed, as it takes lists of likelihoods)

### Endpoint
/powerlaw/loglikelihood_ratio

### Parameters
#### Request Body
- **loglikelihoods1** (list or array) - Required - The logarithms of the likelihoods of each observation, calculated from a particular probability distribution.
- **loglikelihoods2** (list or array) - Required - The logarithms of the likelihoods of each observation, calculated from a particular probability distribution.
- **nested** (bool) - Optional - Whether one of the two probability distributions that generated the likelihoods is a nested version of the other. False by default.
- **normalized_ratio** (bool) - Optional - Whether to return the loglikelihood ratio, R, or the normalized ratio R/sqrt(n*variance).

### Response
#### Success Response (200)
- **R** (float) - The loglikelihood ratio of the two sets of likelihoods. If positive, the first set of likelihoods is more likely. If negative, the reverse is true.
- **p** (float) - The significance of the sign of R. If below a critical value (typically .05) the sign of R is taken to be significant.

### Response Example
```json
{
  "R": 2.5,
  "p": 0.01
}
```
```

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

### Powerlaw Class: Fit

Source: https://pythonhosted.org/powerlaw/genindex.html

Represents a fitted powerlaw distribution and provides methods for comparison and analysis.

```APIDOC
## Class: powerlaw.Fit

### Description

A class that holds the results of fitting a powerlaw distribution to data. It offers methods for comparing distributions, calculating likelihoods, and plotting.

### Methods

- **ccdf()**
  - Description: Returns the Complementary Cumulative Distribution Function (CCDF) of the fitted distribution.

- **cdf()**
  - Description: Returns the Cumulative Distribution Function (CDF) of the fitted distribution.

- **distribution_compare(other_fit, **kwargs)**
  - Description: Compares this fit to another `Fit` object.

- **find_xmin()**
  - Description: Finds the optimal `xmin` value for the powerlaw fit.

- **loglikelihood_ratio(other_fit, **kwargs)**
  - Description: Computes the log-likelihood ratio between this fit and another `Fit` object.

- **nested_distribution_compare(other_fit, **kwargs)**
  - Description: Performs a nested comparison between this fit and another `Fit` object.

- **nested_loglikelihood_ratio(other_fit, **kwargs)**
  - Description: Computes the nested log-likelihood ratio between this fit and another `Fit` object.

- **pdf()**
  - Description: Returns the Probability Density Function (PDF) of the fitted distribution.

- **plot_ccdf(**kwargs)**
  - Description: Plots the Complementary Cumulative Distribution Function (CCDF) of the fitted distribution.

- **plot_cdf(**kwargs)**
  - Description: Plots the Cumulative Distribution Function (CDF) of the fitted distribution.

- **plot_pdf(**kwargs)**
  - Description: Plots the Probability Density Function (PDF) of the fitted distribution.
```

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

### Powerlaw Module Functions

Source: https://pythonhosted.org/powerlaw/genindex.html

This section details the functions available directly within the powerlaw module.

```APIDOC
## Module: powerlaw

### Functions

- **bisect_map()**
  - Description: Maps values to their bisect index.

- **cdf(data, **kwargs)**
  - Description: Computes the Cumulative Distribution Function (CDF).
  - Usage: Can be used as a method of `powerlaw.Distribution` or `powerlaw.Fit` objects.

- **checkunique(data)**
  - Description: Checks if all elements in the data are unique.

- **cumulative_distribution_function(data, **kwargs)**
  - Description: Alias for `cdf()`.

- **fit(data, **kwargs)**
  - Description: Fits a powerlaw distribution to the given data.
  - Usage: Can be used as a method of `powerlaw.Distribution` objects.

- **is_discrete(data)**
  - Description: Determines if the data represents a discrete distribution.

- **pdf(data, **kwargs)**
  - Description: Computes the Probability Density Function (PDF).
  - Usage: Can be used as a method of `powerlaw.Distribution` or `powerlaw.Fit` objects.

- **plot_ccdf(data, **kwargs)**
  - Description: Plots the Complementary Cumulative Distribution Function (CCDF).
  - Usage: Can be used as a method of `powerlaw.Distribution` or `powerlaw.Fit` objects.

- **plot_cdf(data, **kwargs)**
  - Description: Plots the Cumulative Distribution Function (CDF).
  - Usage: Can be used as a method of `powerlaw.Distribution` or `powerlaw.Fit` objects.

- **plot_pdf(data, **kwargs)**
  - Description: Plots the Probability Density Function (PDF).
  - Usage: Can be used as a method of `powerlaw.Distribution` or `powerlaw.Fit` objects.

- **trim_to_range(data, min_val, max_val)**
  - Description: Trims the data to be within the specified minimum and maximum values.
```

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

### powerlaw.plot_pdf

Source: https://pythonhosted.org/powerlaw/index.html

Plots the probability density function (PDF) of the data.

```APIDOC
## powerlaw.plot_pdf

### Description
Plots the probability density function (PDF) to a new figure or to axis ax if provided.

### Method
Not applicable (function call)

### Endpoint
Not applicable (function call)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Parameters
- **data** (list or array) - Required - The input data.
- **ax** (matplotlib axis, optional) - The axis to which to plot. If None, a new figure is created.
- **linear_bins** (bool, optional) - Whether to use linearly spaced bins (True) or logarithmically spaced bins (False). False by default.

### Request Example
```python
import powerlaw
import matplotlib.pyplot as plt
data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
ax = powerlaw.plot_pdf(data)
plt.show()
```

### Response
#### Success Response (200)
- **ax** (matplotlib axis) - The axis to which the plot was made.

#### Response Example
(Returns a matplotlib axis object, no JSON representation)
```

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

### plot_ccdf

Source: https://pythonhosted.org/powerlaw/index.html

Plots the Complementary Cumulative Distribution Function (CCDF).

```APIDOC
## plot_ccdf

### Description
Plots the CCDF to a new figure or to axis ax if provided.

### Parameters
#### Request Body
- **ax** (matplotlib axis) - Optional - The axis to which to plot.
- **original_data** (bool) - Optional - Whether to use all of the data initially passed to the Fit object.
- **survival** (bool) - Optional - Whether to plot a CDF (False) or CCDF (True). True by default.
```

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

### powerlaw.nested_loglikelihood_ratio

Source: https://pythonhosted.org/powerlaw/index.html

Calculates a loglikelihood ratio and the p-value, assuming one distribution is nested within the other.

```APIDOC
## powerlaw.nested_loglikelihood_ratio

### Description
Calculates a loglikelihood ratio and the p-value for testing which of two probability distributions is more likely to have created a set of observations. Assumes one of the probability distributions is a nested version of the other.

### Method
POST (assumed, as it takes lists of likelihoods)

### Endpoint
/powerlaw/nested_loglikelihood_ratio

### Parameters
#### Request Body
- **loglikelihoods1** (list or array) - Required - The logarithms of the likelihoods of each observation, calculated from a particular probability distribution.
- **loglikelihoods2** (list or array) - Required - The logarithms of the likelihoods of each observation, calculated from a particular probability distribution.
- **nested** (bool) - Optional - Whether one of the two probability distributions that generated the likelihoods is a nested version of the other. True by default.
- **normalized_ratio** (bool) - Optional - Whether to return the loglikelihood ratio, R, or the normalized ratio R/sqrt(n*variance).

### Response
#### Success Response (200)
- **R** (float) - The loglikelihood ratio of the two sets of likelihoods. If positive, the first set of likelihoods is more likely. If negative, the reverse is true.
- **p** (float) - The significance of the sign of R. If below a critical value (typically .05) the sign of R is taken to be significant.

### Response Example
```json
{
  "R": 1.8,
  "p": 0.03
}
```
```

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

### powerlaw.pdf

Source: https://pythonhosted.org/powerlaw/index.html

Calculates the probability density function (normalized histogram) of the data.

```APIDOC
## powerlaw.pdf

### Description
Returns the probability density function (normalized histogram) of the data.

### Method
Not applicable (function call)

### Endpoint
Not applicable (function call)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Parameters
- **data** (list or array) - Required - The input data.
- **xmin** (float, optional) - Minimum value of the PDF. If None, uses the smallest value in the data.
- **xmax** (float, optional) - Maximum value of the PDF. If None, uses the largest value in the data.
- **linear_bins** (bool, optional) - Whether to use linearly spaced bins, as opposed to logarithmically spaced bins (recommended for log-log plots).

### Request Example
```python
import powerlaw
data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
bin_edges, probabilities = powerlaw.pdf(data)
```

### Response
#### Success Response (200)
- **bin_edges** (array) - The edges of the bins of the probability density function.
- **probabilities** (array) - The portion of the data that is within the bin. Length 1 less than bin_edges, as it corresponds to the spaces between them.

#### Response Example
```json
{
  "bin_edges": [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0],
  "probabilities": [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1]
}
```
```

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

### Plot CDF

Source: https://pythonhosted.org/powerlaw/index.html

Plots the Cumulative Distribution Function (CDF) of the theoretical distribution.

```APIDOC
## Plot CDF

### Description
Plots the cumulative distribution function (CDF) of the theoretical distribution for the values given in data within xmin and xmax, if present. Plots to a new figure or to axis ax if provided.

### Method
`plot_cdf`

### Parameters
#### Parameters
- **data** (list or array, optional) - If not provided, attempts to use the data from the Fit object in which the Distribution object is contained.
- **ax** (matplotlib axis, optional) - The axis to which to plot. If None, a new figure is created.
- **survival** (bool, optional) - Whether to plot a CDF (False) or CCDF (True). False by default.

### Returns
- **ax** (matplotlib axis) - The axis to which the plot was made.
```

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

### Powerlaw Class: Distribution

Source: https://pythonhosted.org/powerlaw/genindex.html

Represents a powerlaw distribution and provides methods for analysis.

```APIDOC
## Class: powerlaw.Distribution

### Description

A class representing a powerlaw distribution. It allows for various statistical analyses and manipulations of powerlaw-distributed data.

### Methods

- **cdf(data, **kwargs)**
  - Description: Computes the Cumulative Distribution Function (CDF) for the distribution.

- **fit(data, **kwargs)**
  - Description: Fits a powerlaw distribution to the given data.
  - Returns: A `powerlaw.Fit` object representing the fitted distribution.

- **generate_random(n)**
  - Description: Generates `n` random numbers from this powerlaw distribution.

- **in_range(x)**
  - Description: Checks if a value `x` falls within the valid range of the distribution.

- **initial_parameters()**
  - Description: Returns the initial parameters for fitting.

- **KS(data)**
  - Description: Computes the Kolmogorov-Smirnov statistic for the data against this distribution.

- **likelihoods(data)**
  - Description: Computes the likelihoods of the data points under this distribution.

- **loglikelihoods(data)**
  - Description: Computes the log-likelihoods of the data points under this distribution.

- **parameter_range()**
  - Description: Returns the valid parameter range for the distribution.

- **pdf(data, **kwargs)**
  - Description: Computes the Probability Density Function (PDF) for the distribution.

- **plot_ccdf(data, **kwargs)**
  - Description: Plots the Complementary Cumulative Distribution Function (CCDF).

- **plot_cdf(data, **kwargs)**
  - Description: Plots the Cumulative Distribution Function (CDF).

- **plot_pdf(data, **kwargs)**
  - Description: Plots the Probability Density Function (PDF).
```

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

### Class: powerlaw.Distribution

Source: https://pythonhosted.org/powerlaw/index.html

An abstract class for theoretical probability distributions. Can be created with particular parameter values, or fitted to a dataset.

```APIDOC
## Class powerlaw.Distribution

### Description
An abstract class for theoretical probability distributions. Can be created with particular parameter values, or fitted to a dataset. Fitting is by maximum likelihood estimation by default.

### Parameters
- **xmin** (int or float) - Optional - The data value beyond which distributions should be fitted.
- **xmax** (int or float) - Optional - The maximum value of the fitted distributions.
- **discrete** (boolean) - Optional - Whether the distribution is discrete (integers).
- **data** (list or array) - Optional - The data to which to fit the distribution.
- **fit_method** ("Likelihood" or "KS") - Optional - Method for fitting the distribution.
- **parameters** (tuple or list) - Optional - The parameters of the distribution.
- **parameter_range** (dict) - Optional - Dictionary of valid parameter ranges for fitting.
- **initial_parameters** (tuple or list) - Optional - Initial values for the parameter in the fitting search.
- **discrete_approximation** ("round", "xmax" or int) - Optional - Estimation method for discrete forms.
- **parent_Fit** (Fit object) - Optional - A Fit object from which to use data.
```

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

### powerlaw.checkunique

Source: https://pythonhosted.org/powerlaw/index.html

Quickly checks if a sorted array is all unique elements.

```APIDOC
## powerlaw.checkunique

### Description
Quickly checks if a sorted array is all unique elements.

### Method
GET (assumed, as it's a check function)

### Endpoint
/powerlaw/checkunique

### Parameters
#### Query Parameters
- **data** (list or array) - Required - The sorted array to check.

### Response
#### Success Response (200)
- **is_unique** (bool) - True if all elements are unique, False otherwise.

### Response Example
```json
{
  "is_unique": true
}
```
```

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

### Plot CCDF

Source: https://pythonhosted.org/powerlaw/index.html

Plots the Complementary Cumulative Distribution Function (CCDF) of the theoretical distribution.

```APIDOC
## Plot CCDF

### Description
Plots the complementary cumulative distribution function (CCDF) of the theoretical distribution for the values given in data within xmin and xmax, if present. Plots to a new figure or to axis ax if provided.

### Method
`plot_ccdf`

### Parameters
#### Parameters
- **data** (list or array, optional) - If not provided, attempts to use the data from the Fit object in which the Distribution object is contained.
- **ax** (matplotlib axis, optional) - The axis to which to plot. If None, a new figure is created.
- **survival** (bool, optional) - Whether to plot a CDF (False) or CCDF (True). True by default.

### Returns
- **ax** (matplotlib axis) - The axis to which the plot was made.
```

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

### powerlaw.ccdf

Source: https://pythonhosted.org/powerlaw/index.html

Calculates the complementary cumulative distribution function (CCDF) of the data.

```APIDOC
## powerlaw.ccdf

### Description
The complementary cumulative distribution function (CCDF) of the data.

### Method
GET (assumed, as it's a calculation function)

### Endpoint
/powerlaw/ccdf

### Parameters
#### Query Parameters
- **data** (list or array) - Optional - The input data.
- **survival** (bool) - Optional - Whether to calculate a CDF (False) or CCDF (True). True by default.

### Response
#### Success Response (200)
- **X** (array) - The sorted, unique values in the data.
- **probabilities** (array) - The portion of the data that is less than or equal to X.

### Response Example
```json
{
  "X": [1, 2, 3, 4, 5],
  "probabilities": [0.8, 0.6, 0.4, 0.2, 0.0]
}
```
```

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

### powerlaw.trim_to_range

Source: https://pythonhosted.org/powerlaw/index.html

Removes elements of the data that are outside the specified range.

```APIDOC
## powerlaw.trim_to_range

### Description
Removes elements of the data that are above xmin or below xmax (if present).

### Method
Not applicable (function call)

### Endpoint
Not applicable (function call)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Parameters
- **data** (list or array) - Required - The input data.
- **xmin** (float, optional) - The minimum value to keep in the data.
- **xmax** (float, optional) - The maximum value to keep in the data.

### Request Example
```python
import powerlaw
data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
trimmed_data = powerlaw.trim_to_range(data, xmin=3, xmax=8)
# trimmed_data will be [3, 4, 5, 6, 7, 8]
```

### Response
#### Success Response (200)
- **trimmed_data** (list or array) - The data with elements outside the specified range removed.

#### Response Example
```json
{
  "trimmed_data": [3, 4, 5, 6, 7, 8]
}
```
```

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

### powerlaw.cdf

Source: https://pythonhosted.org/powerlaw/index.html

Calculates the cumulative distribution function (CDF) of the data.

```APIDOC
## powerlaw.cdf

### Description
The cumulative distribution function (CDF) of the data.

### Method
GET (assumed, as it's a calculation function)

### Endpoint
/powerlaw/cdf

### Parameters
#### Query Parameters
- **data** (list or array) - Optional - The input data.
- **survival** (bool) - Optional - Whether to calculate a CDF (False) or CCDF (True). False by default.

### Response
#### Success Response (200)
- **X** (array) - The sorted, unique values in the data.
- **probabilities** (array) - The portion of the data that is less than or equal to X.

### Response Example
```json
{
  "X": [1, 2, 3, 4, 5],
  "probabilities": [0.2, 0.4, 0.6, 0.8, 1.0]
}
```
```

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

### powerlaw.cumulative_distribution_function

Source: https://pythonhosted.org/powerlaw/index.html

The cumulative distribution function (CDF) of the data, with options for xmin and xmax.

```APIDOC
## powerlaw.cumulative_distribution_function

### Description
The cumulative distribution function (CDF) of the data.

### Method
GET (assumed, as it's a calculation function)

### Endpoint
/powerlaw/cumulative_distribution_function

### Parameters
#### Query Parameters
- **data** (list or array) - Optional - The input data.
- **xmin** (int or float) - Optional - The minimum data size to include. Values less than xmin are excluded.
- **xmax** (int or float) - Optional - The maximum data size to include. Values greater than xmax are excluded.
- **survival** (bool) - Optional - Whether to calculate a CDF (False) or CCDF (True). False by default.

### Response
#### Success Response (200)
- **X** (array) - The sorted, unique values in the data.
- **probabilities** (array) - The portion of the data that is less than or equal to X.

### Response Example
```json
{
  "X": [10, 20, 30],
  "probabilities": [0.3, 0.7, 1.0]
}
```
```

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

### powerlaw.plot_cdf

Source: https://pythonhosted.org/powerlaw/index.html

Plots the cumulative distribution function (CDF) of the data.

```APIDOC
## powerlaw.plot_cdf

### Description
Plots the cumulative distribution function (CDF) of the data to a new figure or to axis ax if provided.

### Method
Not applicable (function call)

### Endpoint
Not applicable (function call)

### Parameters
#### Path Parameters
None

#### Query Parameters
None

#### Request Body
None

### Parameters
- **data** (list or array) - Required - The input data.
- **ax** (matplotlib axis, optional) - The axis to which to plot. If None, a new figure is created.
- **survival** (bool, optional) - Whether to plot a CDF (False) or CCDF (True). False by default.

### Request Example
```python
import powerlaw
import matplotlib.pyplot as plt
data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
ax = powerlaw.plot_cdf(data)
plt.show()
```

### Response
#### Success Response (200)
- **ax** (matplotlib axis) - The axis to which the plot was made.

#### Response Example
(Returns a matplotlib axis object, no JSON representation)
```

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

### powerlaw.is_discrete

Source: https://pythonhosted.org/powerlaw/index.html

Checks if every element of the array is an integer.

```APIDOC
## powerlaw.is_discrete

### Description
Checks if every element of the array is an integer.

### Method
GET (assumed, as it's a check function)

### Endpoint
/powerlaw/is_discrete

### Parameters
#### Query Parameters
- **data** (list or array) - Required - The array to check.

### Response
#### Success Response (200)
- **is_discrete** (bool) - True if all elements are integers, False otherwise.

### Response Example
```json
{
  "is_discrete": false
}
```
```
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