@misc{clauset2007powerlaw,
  abstract = {Power-law distributions occur in many situations of scientific interest and
have significant consequences for our understanding of natural and man-made
phenomena. Unfortunately, the detection and characterization of power laws is
complicated by the large fluctuations that occur in the tail of the
distribution -- the part of the distribution representing large but rare events
-- and by the difficulty of identifying the range over which power-law behavior
holds. Commonly used methods for analyzing power-law data, such as
least-squares fitting, can produce substantially inaccurate estimates of
parameters for power-law distributions, and even in cases where such methods
return accurate answers they are still unsatisfactory because they give no
indication of whether the data obey a power law at all. Here we present a
principled statistical framework for discerning and quantifying power-law
behavior in empirical data. Our approach combines maximum-likelihood fitting
methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic
and likelihood ratios. We evaluate the effectiveness of the approach with tests
on synthetic data and give critical comparisons to previous approaches. We also
apply the proposed methods to twenty-four real-world data sets from a range of
different disciplines, each of which has been conjectured to follow a power-law
distribution. In some cases we find these conjectures to be consistent with the
data while in others the power law is ruled out.},
  author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
  doi = {10.1137/070710111},
  interhash = {2e3bc5bbd7449589e8bfb580e8936d4b},
  intrahash = {7da1624e601898dd74df839ce2daeb24},
  note = {cite arxiv:0706.1062Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at  http://www.santafe.edu/~aaronc/powerlaws/},
  title = {Power-law distributions in empirical data},
  url = {http://arxiv.org/abs/0706.1062},
  year = 2007
}

@article{Goldstein04powerlawfitV1,
  abstract = {Version 1 of Goldstein 04 power law fit containing also the chi 2 test},
  author = {Goldstein, M. L. and Morris, S. A. and Yen, G. G.},
  interhash = {6216b964a64c9783e3bc22f46fa98a20},
  intrahash = {ce8d5ffe96977fd45bd01d677e9cc17d},
  journal = {The European Physical Journal B - Condensed Matter and Complex Systems},
  number = 2,
  pages = {255-258},
  title = {Fitting to the power-law distribution},
  url = {http://arxiv.org/abs/cond-mat/0402322v1},
  volume = 41,
  year = 2004
}

@article{newman05power,
  author = {Newman, M. E. J.},
  interhash = {7539b701d6df3fb9a90b0ff70a32bfe9},
  intrahash = {436d9c707f94b26bbee4187fdf714820},
  journal = {Contemporary Physics},
  pages = 323,
  title = {Power laws, Pareto distributions and Zipf's law},
  url = {doi:10.1080/00107510500052444},
  volume = 46,
  year = 2005
}

@incollection{alfi07howpeople,
  abstract = {In Fig. 1 we show the number of registrations to Statphys 23 
(full dots).
Each point corresponds to one day and the deadline $T^*$=March 31 was
the one corresponding to the early registration and abstract submission.
We also plot the data corresponding to the a different conference
(EP2DS 17)
for which we have rescaled the total number of registration at its
own $T^*$.
The data of the two conferences are remarkably similar
and are characterized by an initial linear behavior followed
by a strong increase near $T^*$.
This strong similarity suggests for a simple mechanism to describe
the response of the people to a deadline and we propose have a 
simple model.
The basic idea is that the pressure you have to register is proportional
to the inverse of the remaining time to the deadline.
This gives a probability, $p(t)$, to register at time $t$ that is $p(t)\propto
\frac 1{(T^*-t)}$.
From this the number of the registrations at time $t$ is:
$$
N(t)=C\int_{0}^{T^*}p(t)\;dt=A(N_{{tot}})\;\ln(\frac{T^*}{T^*-t}).
\nonumber
$$
The logarithmic singularity at the end is regularized by discretizing the 
integral with an interval of one day and the constant $A(N_{tot})$
is fixed by the total number of final registration $N_{tot}$.
As one can see in Fig. 1 this simple model fits the
observed behavior extremely well.
This permits to predict the total number of registrations
already from the initial slope.
A result that could have  some practical interest.
The model only assumes that the probability to register
is the same for the whole interval of the the remaining time.
In this respect there is no real tendency to shift the registration 
towards the deadline.
The increase of pressure is just due to the approaching of the deadline.
This situation may appear curious because one could have expected
a stronger pressure to postpone the payment towards the deadline.
In this respect, however, one should notice that the data in Fig. 1
refer only to the registration and not to the payment of the fee which
could have been done also at a late time.},
  address = {Genova, Italy},
  author = {Alfi, V. and Parisi, G. and Pietronero, L.},
  booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
  editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
  interhash = {b8a6f0dce8a510ad5051de14bab46484},
  intrahash = {618251cde1e99f37344c378d4ff81cbc},
  month = {9-13 July},
  title = {How People React to a Deadline: The Distribution of Registrations of Statphys 23},
  url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1122},
  year = 2007
}