Distribution fitting

In Timothy Sturm's example, we claim that the histogram of some data seemed to fit a normal distribution. SciPy has a few routines to help us approximate the best distribution to a random variable, together with the parameters that best approximate this fit. For example, for the data in that problem, the mean and standard deviation of the normal distribution that realizes the best fit can be found in the following way:

>>> from scipy.stats import norm     # Gaussian distribution
>>> mean,std=norm.fit(dataDiff)

We can now plot the (normed) histogram of the data, together with the computed probability density function, as follows:

>>> plt.hist(dataDiff, normed=1)
>>> x=numpy.linspace(dataDiff.min(),dataDiff.max(),1000)
>>> pdf=norm.pdf(x,mean,std)
>>> plt.plot(x,pdf)
>>> plt.show()

We will obtain the following graph showing the maximum likelihood estimate to the normal distribution that best fits dataDiff:

We...