2. fitter module

main module of the fitter package

Section author: Thomas Cokelaer, Aug 2014

class Fitter(data, xmin=None, xmax=None, bins=100, distributions=None, verbose=True, timeout=10)

Fit a data sample to known distributions

A naive approach often performed to figure out the undelying distribution that could have generated a data set, it to compare the histogram of the data with a PDF (probability distribution function) of a known distribution (e.g., normal).

Yet, the parameters of the distribution are not known and there are lots of distributions. Therefore, an automatic way to fit many distributions to the data would be useful, which is what is implemented here.

Given a data sample, we use the fit method of SciPy to extract the parameters of that distribution that best fit the data. We repeat this for all available distributions. Finally, we provide a summary so that one can see the quality of the fit for those distributions

Here is an example where we generate a sample from a gamma distribution.

>>> # First, we create a data sample following a Gamma distribution
>>> from scipy import stats
>>> data = stats.gamma.rvs(2, loc=1.5, scale=2, size=20000)

>>> # We then create the Fitter object
>>> import fitter
>>> f = fitter.Fitter(data)

>>> # just a trick to use only 10 distributions instead of 80 to speed up the fitting
>>> f.distributions = f.distributions[0:10] + ['gamma']

>>> # fit and plot
>>> f.fit()
>>> f.summary()
        sumsquare_error
gamma          0.000095
beta           0.000179
chi            0.012247
cauchy         0.044443
anglit         0.051672
[5 rows x 1 columns]

Once the data has been fitted, the summary() metod returns a sorted dataframe where the

Looping over the 80 distributions in SciPy could takes some times so you can overwrite the distributions with a subset if you want. In order to reload all distributions, call load_all_distributions().

Some distributions to not converge when fitting. There is a timeout of 10 seconds after which the fitting procedure is cancelled. You can change this timeout attribute if needed.

If the histogram of the data has outlier of very long tails, you may want to increase the bins binning or to ignore data below or above a certain range. This can be achieved by setting the xmin and xmax attributes. If you set xmin, you can come back to the original data by setting xmin to None (same for xmax) or just recreate an instance.

Constructor

Parameters:

• data (list) – a numpy array or a list
• xmin (float) – if None, use the data minimum value, otherwise histogram and fits will be cut
• xmax (float) – if None, use the data maximum value, otherwise histogram and fits will be cut
• bins (int) – numbers of bins to be used for the cumulative histogram. This has an impact on the quality of the fit.
• distributions (list) – give a list of distributions to look at. IF none, use all scipy distributionsthat have a fit method.
• verbose (bool) –
• timeout – max time for a given distribution. If timeout is reached, the distribution is skipped.

distributions = None

list of distributions to test

fit()

Loop over distributions and find best parameter to fit the data for each

When a distribution is fitted onto the data, we populate a set of dataframes:

• df_errors :sum of the square errors between the data and the fitted distribution i.e.,
• fitted_param : the parameters that best fit the data
• fitted_pdf : the PDF generated with the parameters that best fit the data

Indices of the dataframes contains the name of the distribution.

get_best()

Return best fitted distribution and its parameters

a dictionary with one key (the distribution name) and its parameters

hist()

Draw normed histogram of the data using bins

(Source code, png, hires.png, pdf)

load_all_distributions()

Replace the distributions attribute with all scipy distributions

plot_pdf(names=None, Nbest=5, lw=2)

Plots Probability density functions of the distributions

Parameters:names (str,list) – names can be a single distribution name, or a list of distribution names, or kept as None, in which case, the first Nbest distribution will be taken (default to best 5)

summary(Nbest=5, lw=2)

Plots the distribution of the data and Nbest distribution

xmax

consider only data below xmax. reset if None

xmin

consider only data above xmin. reset if None