Fitting a curve to a power-law distribution with curve_fit does not work

Question

I am trying to find a curve fitting my data that visually seem to have a power law distribution.

I hoped to utilize scipy.optimize.curve_fit, but no matter

Answer 1

Your func_powerlaw is not strictly a power law, as it has an additive constant.

Generally speaking, if you want a quick visual appraisal of a power law relation, you would

plot(log(x),log(y))

or

loglog(x,y)

Both of them should give a straight line, although there are subtle differences among them (in particular, regarding curve fitting).

All this without the additive constant, which messes up the power law relation.

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If you want to fit a power law that weighs data according to the log-log scale (typically desirable), you can use code below.

import numpy as np
from scipy.optimize import curve_fit

def powlaw(x, a, b) :
    return a * np.power(x, b)
def linlaw(x, a, b) :
    return a + x * b

def curve_fit_log(xdata, ydata) :
    """Fit data to a power law with weights according to a log scale"""
    # Weights according to a log scale
    # Apply fscalex
    xdata_log = np.log10(xdata)
    # Apply fscaley
    ydata_log = np.log10(ydata)
    # Fit linear
    popt_log, pcov_log = curve_fit(linlaw, xdata_log, ydata_log)
    #print(popt_log, pcov_log)
    # Apply fscaley^-1 to fitted data
    ydatafit_log = np.power(10, linlaw(xdata_log, *popt_log))
    # There is no need to apply fscalex^-1 as original data is already available
    return (popt_log, pcov_log, ydatafit_log)