Match Up a Histogram and a Normal Distribution

2013 June 13

Given some data that have been histogrammed, how do we overplot the normal distribution that represents the maximum likelihood parameters of the underlying unbinned data? The key is getting the normalization right, and the key to that is that we can compute the area under both the histogram and the distribution.

Given data d and nbins:

m = d.mean()
s = d.std()
xmin = d.min()  # these bounds can be tweaked
xmax = d.max()
x = np.linspace(xmin, xmax, 512)  # the 512 is also adjustable
norm = d.size * (xmax - xmin) / (nbins * np.sqrt(2 * np.pi) * s)
y = norm * np.exp(-0.5 * ((x - m) / s)**2)