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Solving Power Law Distribution in Python

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问题 I have data that closely resembles a power law distribution. Using Python, I want to approximate the data by solving two equations in the form: y is the y axis data. In Python it would be data[i] . x would be i + 1 . It follows that we get two equations with two unknown variables at the first data index and at a "random" 2nd one somewhere else in the data: The problem comes down to solving just due to mathematical simplification. I don't know how to solve an equation like this using libraries

Solving Power Law Distribution in Python

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python plot and powerlaw fit

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问题 I have the following list: [6, 4, 0, 0, 0, 0, 0, 1, 3, 1, 0, 3, 3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 3, 2, 3, 3, 2, 5, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 3, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 2, 3, 2, 1, 0, 0, 0, 1, 2] I want to plot the frequency of each entity with python and make a powerlaw analysis on it. But I cannot figure how I can plot the list with ylabel the frequency and

How to plot CCDF graph on a logarithmic scale?

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问题 I want to plot a CCDF graph for some of my simulated power-law tail data on a log-log axis, below is my R code of plotting a CCDF graph on a normal axis, I used the code on the link: (How to plot a CCDF gragh?) > load("fakedata500.Rda") > x<-fakedata500 > f<-ecdf(x) > f Empirical CDF Call: ecdf(x) x[1:500] = 0.50174, 0.50307, 0.50383, ..., 81.674, 140.63 > plot(f) Below is the ECDF graph: > plot(sort(x), 1-f(sort(x)), type="s", lwd=1) and this command gives me the CCDF graph: However, I would

Input to fit a power-law to degree distribution of a network

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问题 I would like to use R to test whether the degree distribution of a network behaves like a power-law with scale-free property. Nonetheless, I've read different people doing this in many different ways, and one confusing point is the input one should use in the model. Barabasi, for example, recommends fitting a power-law to the 'complementary cumulative distribution' of degrees (see Advanced Topic 3.B of chapter 4, figure 4.22). However, I've seen people fit a power-law to the degrees of the

how to plot degree distribution in R

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问题 I would like to know whether the output of a script to plot a degree distribution can be correct. So the script is ( where the vector with the degrees of all my vertices is stored in x): x is x [1] 7 9 8 5 6 2 8 9 7 5 2 4 6 9 2 6 10 8 x is the degree of a certain network vertice - like vertice 1 has degree 7, vertice 2 has degree 9 and so on x <- v2 summary(x) library(igraph) split.screen(c(1,2)) screen(1) plot (tabulate(x), log = "xy", ylab = "Frequency (log scale)", xlab = "Degree (log

Power Law Fit of cut-off distribution with the poweRlaw package

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问题 I am currently trying to find a way to calculate a power-law fit for a cut-off distribution with MLE. The distribution looks as follows: As you can see, I was able to fit the whole distribution (Power-law fit) and also the lower bound (exp-fit) separately. What I am failing to figure out, is how to fit the upper bound of the distribution (f.e. 8 < x < 100). Is there any way to do this with the poweRlaw package or any other R package? What I am hoping for is something looking like this (note:

Python power law fit with upper limits & asymmetric errors in data using ODR

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问题 I'm trying to fit some data to a power law using python. The problem is that some of my points are upper limits, which I don't know how to include in the fitting routine. In the data, I have put the upper limits as errors in y equal to 1, when the rest is much smaller. You can put this errors to 0 and change the uplims list generator, but then the fit is terrible. The code is the following: import numpy as np import matplotlib.pyplot as plt from scipy.odr import * # Initiate some data x = [1

Python power law fit with upper limits & asymmetric errors in data using ODR

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I'm trying to fit some data to a power law using python. The problem is that some of my points are upper limits, which I don't know how to include in the fitting routine. In the data, I have put the upper limits as errors in y equal to 1, when the rest is much smaller. You can put this errors to 0 and change the uplims list generator, but then the fit is terrible. The code is the following: import numpy as np import matplotlib.pyplot as plt from scipy.odr import * # Initiate some data x = [1.73e-04, 5.21e-04, 1.57e-03, 4.71e-03, 1.41e-02, 4.25e-02, 1.28e-01, 3.84e-01, 1.15e+00] x_err = [1e-04,

How can I generate a sample from a log-normal distribution with Pareto tail in R?

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I would like to generate a sample from a log-normal distribution with Pareto tail in R. Can somebody help me? Thanks. I'm not sure this is what you're looking for, but there is a fair amount of literature on the topic of Double Pareto Log-normal Distributions, or so-ca.led dPlN. See this , and this , and this . These are used to simulate everything from the distribution of earnings and income, to oil field size, to internet traffic . If this is not what you're looking for, let me know and I'll delete the post. You ask how to generate a random sample from dPlN. Theoretically, it is possible to