poweRlaw | package implements both the discrete and continuous maximum
kandi X-RAY | poweRlaw Summary
kandi X-RAY | poweRlaw Summary
This package implements both the discrete and continuous maximum likelihood estimators for fitting the power-law distribution to data using the methods described in Clauset et al, 2009. It also provides function to fit log-normal and Poisson distributions. Additionally, a goodness-of-fit based approach is used to estimate the lower cut-off for the scaling region. The code developed in this package was influenced from the python and R code found at Aaron Clauset’s website. In particular, the R code of Laurent Dubroca and Cosma Shalizi.
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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:
QUESTION
I am using the R package "poweRlaw" to estimate and subsequently draw from discrete power law distributions, however the distribution drawn from the fit does not seem to match the data. To illustrate, consider this example from a guide for this package: https://cran.r-project.org/web/packages/poweRlaw/vignettes/b_powerlaw_examples.pdf. Here we first download an example dataset from the package and then fit a discrete power law.
...ANSWER
Answered 2021-Apr-05 at 15:58So there's a few things going on here.
As you hinted at in your question, if you want to compare distributions, you need to truncate moby, so
moby = moby[moby >= m_pl$getXmin()]
Using
density()
is a bit fraught. This is a kernel density smoother, that draws Normal distributions over discrete points. As the powerlaw has a very long tail, this is suspectComparing the tails of two powerlaw distributions is tricky (simulate some data and see).
Anyway, if you run
QUESTION
I have a txt output file that I would like to store some of the values in lines.
...ANSWER
Answered 2020-May-04 at 09:56With
if line=="PhoIndex"
you're checking if the line is EQUAL to that string. You should rather verify if the checked line CONTAINS that string, by using
if "PhoIndex" in line:
to open your loop. Then, you could transform the line into a list, by separating the string elements on each space, like so:
line_array = line.split(" ")
Then, given that your numbers are always the third and second element of this list if it's the PhoIndex line, you can use
line_array.pop() ## remove the last element
line_array.pop(0)
line_array.pop(0) ## remove the first two elements
And then simply do this for every row, by using the respective string to query for the type of row (as with "PhoIndex") and the corresponding list pops according to the line structures. This works if your txt file always has a regular structure. If not then simply proceed in the same way until the split
method, and then just retrieve the elements of the created list you need via characteristics that differentiate them from all the rest, like containing a period character, or whatever.
All left is the definition of an empty template dictionary, as you did above "before the loop", and then assign the lists you obtained as values of their respective dictionary keys. done.
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