Fitting a weighted histogram with a normal distribution

Question

I know how to fit the data entering an histogram with a normal distribution using the SCipy library ( Fitting a histogram with python ) but how could I do the same if on top of having data I have an array of weights having the same dimension. Is there a proper function for that or should I create a second array fed by the data and weighting it myself?

Cheers.

Edit:

This is pretty much already answered here:

Weighted standard deviation in NumPy?

Answer 1

just use the weights paramater on scipy.histogram and pass in your array of weights:

scipy.stats.histogram(a, numbins=10, defaultlimits=None, weights=None, printextras=False)

from the docs:

weights : array_like, optional The weights for each value in a. Default is None, which gives each value a weight of 1.0

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NOTE: as of v1.0, scipy does not have the function histogram , but as of v1.11 histogram appears in numpy , with a similar (but not identical) call signature that includes the weights= argument:

numpy.histogram(a, bins=10, range=None, normed=False, weights=None, density=None)

Answer 2

If you are looking for a Normal distribution N(mu, sigma) you can calculate exactly mu and sigma from the input data.

For example: X = x1,...,xN are the values and W = w1,..., wN their weights

mu = sum (X * W) / sum(W)
sigma = np.sqrt (sum (W * (X- mu)**2) / sum(W))

If you are to fit another kind of distribution, I suggested an answer here using OpenTURNS library.