pdf-distribution for values <1 about powerlaw

[jeffalstott]

Thank you very much for considering this use case and writing a solution
for it!

Can you make this edit as a pull request? It may also be worth testing out
some; I can see in the code a reference to xmax2, which is not defined. As
a lower priority, I would also consider if there's a way to do this without
making another copy of the data; some users have very large datasets and
making another copy of the data can get burdensome.

On Sat, May 14, 2016 at 10:38 PM, Cils [email protected] wrote:

I noticed, that the values below 1 are not included in the
pdf-distribution of the data (powerlow.pdf(), fit.plot_pdf()). For some
reason unknown to me, the histogram logarithmic spaced bins boundaries are
transformed to integers.

line 1952 in powerlaws.py: bins=unique( floor(logspace( log_min_size,
log_max_size, num=number_of_bins)))
In this way a potential infinite number of bins are eliminated.

I modified the function "pdf" to solve the problem. The data are rescaled
by multipling them by xmin before the histogram is computed. At the end the
bins boundareies "edges" are transformed back to the original scale and
returned.

Below the code:

`def pdf(data, xmin=None, xmax=None, linear_bins=False, **kwargs):
"""
Returns the probability density function (normalized histogram) of the
data. Version modified by A.Capelli, include values x<1 in the pdf
distribution.

Parameters

data : list or array
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 : float, optional
Whether to use linearly spaced bins, as opposed to logarithmically
spaced bins (recommended for log-log plots).

Returns

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.
"""
from numpy import logspace, histogram, floor, unique
from math import ceil, log10
if not xmax:
xmax = max(data)
if not xmin:
xmin = min(data)

normalize data to xmin, allow to have pdf also from the data below x=1, modification by A.Capelli

data2=data/xmin
xmax=xmax/xmin
xmin_old=xmin
xmin=1

if linear_bins:
bins = range(int(xmin), int(xmax2))
else:
log_min_size = log10(xmin)
log_max_size = log10(xmax)
number_of_bins = ceil((log_max_size-log_min_size)*10)
bins=unique(
floor(
logspace(
log_min_size, log_max_size, num=number_of_bins)))
hist, edges = histogram(data2, bins, density=True)

transform data back to original

xmax=xmax_xmin_old
xmin=xmin_old
edges=edges_xmin
print(xmin)
return edges, hist`

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