powerlaws | Java library for the analysis of power law distributed data | Data Visualization library
kandi X-RAY | powerlaws Summary
kandi X-RAY | powerlaws Summary
This is a small java library for the analysis of power law distributed data. The methods implemented are all taken form the paper Power-Law Distributions in Empirical Data by Clauset, Shalizi and Newman (2007) and its reference implementations available at It contains facilities for estimating parameters, uncertainty and significance and for generating power law distributed data. All methods are implemented for continuous data, discrete data and the approximation of discrete data with a continuous distribution.
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- Calculates Uncertainties for a given set of data
- Returns the standard deviation of the list of numbers
- Returns a series of integers starting from a specific value
- Returns the mean value of a list of numbers
- Calculates Uncertainties from the given data
- Creates a fit from a collection
- Runs the KDF test
- Returns a cumulative histogram of data
- Tests a set of integers
- Walks through a series of Data
- Estimates the uncertainties of the given data
- Computes the cumulative distribution function
- Returns the probability of x
- Computes the powerLaw with the given dataSamples
- Computes the power of an integer
- Fits the distribution with the given dataSamples
- Generate integer
- Computes the PowerLaw with the given dataSamples
- Calculates the cumulative probability of the given data
- Generates a random value
- Calculates the CDF of the given integer
- Returns the cumulative probability of the given integer
- Returns the probability of the given x
- Sorts the collection
- Generates a list of points
- Compares two numbers
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QUESTION
ANSWER
Answered 2022-Mar-06 at 00:14In this case, the answer is simple.
The integral of a * x**(a - 1) + b * x**(b - 1)
over the interval [0, 1]
is simply 2, suggesting that this distribution is a mixture of two power-law distributions, one of which is drawn with the same probability as the other.* Specifically, your distribution has the following density function:
(a * x**(a - 1))/2 + (b * x**(b - 1))/2
.
Then, a simple algorithm to sample from this distribution is:
- Generate
u
, a uniform random variate in [0, 1]. - With probability 1/2, return
u**(1/a)
. Otherwise, returnu**(1/b)
.
Code follows:
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