I have two arrays. x is the independent variable, and counts is the number of counts of x occurring, like a histogram. I know I can calculate the mean by defining a function:
def mean(x, counts):
return np.sum(x*counts) / np.sum(counts)
Is there a general function I can use to calculate each moment from the distribution defined by x and counts? I would also like to compute the variance.
You could use the moment function from SciPy. It calculates the n-th central moment of your data.
You could also define your own function, which could look something like this:
def nmoment(x, counts, c, n):
return np.sum(counts*(x-c)**n) / np.sum(counts)
In that function, c is meant to be the point around which the moment is taken, and n is the order. So to get the variance, you could do nmoment(x, counts, np.average(x, weights=counts), 2).