def power_law_fit(data, xmin=None, method="auto", return_alpha_only=False):
"""Fitting a power-law distribution to empirical data
@param data: the data to fit, a list containing integer values
@param xmin: the lower bound for fitting the power-law. If C{None},
the optimal xmin value will be estimated as well. Zero means that
the smallest possible xmin value will be used.
@param method: the fitting method to use. The following methods are
implemented so far:
- C{continuous}, C{hill}: exact maximum likelihood estimation
when the input data comes from a continuous scale. This is
known as the Hill estimator. The statistical error of
this estimator is M{(alpha-1) / sqrt(n)}, where alpha is the
estimated exponent and M{n} is the number of data points above
M{xmin}. The estimator is known to exhibit a small finite
sample-size bias of order M{O(n^-1)}, which is small when
M{n > 100}. igraph will try to compensate for the finite sample
size if n is small.
- C{discrete}: exact maximum likelihood estimation when the
input comes from a discrete scale (see Clauset et al among the
references).
- C{auto}: exact maximum likelihood estimation where the continuous
method is used if the input vector contains at least one fractional
value and the discrete method is used if the input vector contains
integers only.
@return: a L{FittedPowerLaw} object. The fitted C{xmin} value and the
power-law exponent can be queried from the C{xmin} and C{alpha}
properties of the returned object.
@newfield ref: Reference
@ref: MEJ Newman: Power laws, Pareto distributions and Zipf's law.
Contemporary Physics 46, 323-351 (2005)
@ref: A Clauset, CR Shalizi, MEJ Newman: Power-law distributions
in empirical data. E-print (2007). arXiv:0706.1062"""
from igraph._igraph import _power_law_fit
if xmin is None or xmin < 0:
xmin = -1
method = method.lower()
if method not in ("continuous", "hill", "discrete", "auto"):
raise ValueError("unknown method: %s" % method)
force_continuous = method in ("continuous", "hill")
fit = FittedPowerLaw(*_power_law_fit(data, xmin, force_continuous))
if return_alpha_only:
from igraph import deprecated
deprecated(
"The return_alpha_only keyword argument of power_law_fit is "
"deprecated from igraph 0.7 and will be removed in igraph 0.8"
)
return fit.alpha
else:
return fit
def power_law_fit(data, xmin=None, method="auto", return_alpha_only=False):
"""Fitting a power-law distribution to empirical data
@param data: the data to fit, a list containing integer values
@param xmin: the lower bound for fitting the power-law. If C{None},
the optimal xmin value will be estimated as well. Zero means that
the smallest possible xmin value will be used.
@param method: the fitting method to use. The following methods are
implemented so far:
- C{continuous}, C{hill}: exact maximum likelihood estimation
when the input data comes from a continuous scale. This is
known as the Hill estimator. The statistical error of
this estimator is M{(alpha-1) / sqrt(n)}, where alpha is the
estimated exponent and M{n} is the number of data points above
M{xmin}. The estimator is known to exhibit a small finite
sample-size bias of order M{O(n^-1)}, which is small when
M{n > 100}. igraph will try to compensate for the finite sample
size if n is small.
- C{discrete}: exact maximum likelihood estimation when the
input comes from a discrete scale (see Clauset et al among the
references).
- C{auto}: exact maximum likelihood estimation where the continuous
method is used if the input vector contains at least one fractional
value and the discrete method is used if the input vector contains
integers only.
@return: a L{FittedPowerLaw} object. The fitted C{xmin} value and the
power-law exponent can be queried from the C{xmin} and C{alpha}
properties of the returned object.
@newfield ref: Reference
@ref: MEJ Newman: Power laws, Pareto distributions and Zipf's law.
Contemporary Physics 46, 323-351 (2005)
@ref: A Clauset, CR Shalizi, MEJ Newman: Power-law distributions
in empirical data. E-print (2007). arXiv:0706.1062"""
from igraph._igraph import _power_law_fit
if xmin is None or xmin < 0:
xmin = -1
method = method.lower()
if method not in ("continuous", "hill", "discrete", "auto"):
raise ValueError("unknown method: %s" % method)
force_continuous = method in ("continuous", "hill")
fit = FittedPowerLaw(*_power_law_fit(data, xmin, force_continuous))
if return_alpha_only:
from igraph import deprecated
deprecated("The return_alpha_only keyword argument of power_law_fit is "\
"deprecated from igraph 0.7 and will be removed in igraph 0.8")
return fit.alpha
else:
return fit
def power_law_fit(data, xmin=None, method="auto", return_alpha_only=True):
"""Fitting a power-law distribution to empirical data
@param data: the data to fit, a list containing integer values
@param xmin: the lower bound for fitting the power-law. If C{None},
the optimal xmin value will be estimated as well. Zero means that
the smallest possible xmin value will be used.
@param method: the fitting method to use. The following methods are
implemented so far:
- C{continuous}, C{hill}: exact maximum likelihood estimation
when the input data comes from a continuous scale. This is
known as the Hill estimator. The statistical error of
this estimator is M{(alpha-1) / sqrt(n)}, where alpha is the
estimated exponent and M{n} is the number of data points above
M{xmin}. The estimator is known to exhibit a small finite
sample-size bias of order M{O(n^-1)}, which is small when
M{n > 100}. igraph will try to compensate for the finite sample
size if n is small.
- C{discrete}: exact maximum likelihood estimation when the
input comes from a discrete scale (see Clauset et al among the
references).
- C{auto}: exact maximum likelihood estimation where the continuous
method is used if the input vector contains at least one fractional
value and the discrete method is used if the input vector contains
integers only.
@param return_alpha_only: whether to return the fitted exponent only.
When this argument is C{True}, the function will return the fitted power-law
exponent only. When C{False}, the function will return a L{FittedPowerLaw}
object with much more details. The default value is C{True} for the time
being for sake of compatibility with earlier releases, but it will be changed
to C{False} from igraph 0.7 onwards.
@return: the fitted exponent or a L{FittedPowerLaw} object, depending on the
value of C{return_alpha_only}.
@newfield ref: Reference
@ref: MEJ Newman: Power laws, Pareto distributions and Zipf's law.
Contemporary Physics 46, 323-351 (2005)
@ref: A Clauset, CR Shalizi, MEJ Newman: Power-law distributions
in empirical data. E-print (2007). arXiv:0706.1062"""
from igraph._igraph import _power_law_fit
if xmin is None or xmin < 0:
xmin = -1
method = method.lower()
if method not in ("continuous", "hill", "discrete", "auto"):
raise ValueError("unknown method: %s" % method)
force_continuous = method in ("continuous", "hill")
fit = FittedPowerLaw(*_power_law_fit(data, xmin, force_continuous))
if return_alpha_only:
from warnings import warn
warn("power_law_fit will return a FittedPowerLaw object from igraph "\
"0.7 onwards. Better prepare for that by setting return_alpha_only "\
"to False when calling power_law_fit()", PendingDeprecationWarning,
stacklevel=3)
return fit.alpha
else:
return fit
