How do I tell how good my exponential curve fit is in SciPy?

Question

I fit some data using Scipy:

param=expon.fit(data)
pdf_fitted=expon.pdf(x,loc=param[-2],scale=param[-1])
plot(x,pdf_fitted,'r')
hist(data,normed=1,alpha=.3,histtype='stepfilled')

And I get a curve that looks like this:

Exponential fit to data

How do I check how good the fit is (is there a parameter for this?). I'd like a number so I can compare different ways of fitting.

Simplest way to go is to use [MSE](http://en.wikipedia.org/wiki/Mean_squared_error). — BartoszKP, Jun 03 '14 at 12:45
Is this question on-topic for SO? It seems to be asking about goodness-of-fit parameters rather than actual programming? — Ffisegydd, Jun 03 '14 at 12:49

score 4 · Accepted Answer · answered Jun 03 '14 at 12:51

The standard method, assuming your errors are normally distributed, is to use the sum of the squared residuals. This, you can turn into rigurours statistics using the chi² distribution.

values, edges = np.histogram(data, bins=np.sqrt(len(data)))
x = edges[:-1] + np.diff(edges)

pdf_fitted = expon.pdf(x, loc=param[0], scale=param[1])
residuals = values - pdf_fitted

print np.dot(residuals, residuals)

Or, if you prefer the RMS:

print np.dot(residuals, residuals) / len(residuals)

How do I tell how good my exponential curve fit is in SciPy?

1 Answers1