Q-Q plots

qq.py

from __future__ import division

import numpy as np
import scipy.stats as stats
from matplotlib import pyplot as plt

def plot(data,cdf=stats.norm.cdf):
    plt.figure()
    plt.plot(np.cumsum(1./len(data) * np.ones(data.shape)),cdf(np.sort(data)),'bx')
    plt.plot((0,1),(0,1),'r-')

    plt.ylim((0,1))
    plt.xlim((0,1))
    plt.xlabel('empirical percentiles')
    plt.ylabel('fit percentiles')

qqplot.m

function qqplot(data,cdf)

    if ~exist('cdf','var'), cdf=@normcdf; end

    figure();
    hold on

    plot(cumsum(1/length(data)*ones(size(data))),cdf(sort(data)),'bx');
    plot([0,1],[0,1],'r-');

    ylim([0,1]);
    xlim([0,1]);
    xlabel('empirical percentiles');
    ylabel('fit percentiles');

    hold off

end

In Matlab, let's generate some data from an exponential

data = exprnd(16,[100,1]);

Now how well does the maximum-likelihood fit exponential distribution fit the data?

qqplot(data,@(x) expcdf(x,mean(data)));

What if we had a lot more data?

data = exprnd(mu,[10000,1]);
qqplot(data,@(x) expcdf(x,mean(data)));

What if we fit some totally bogus distributions?

qqplot(data,@(x) normcdf(x,mean(data)));
qqplot(data,@(x) normcdf(x,mean(data),std(data)));

OKAY technically these are P-P plots

This is good. I don't understand, why SciPy doesn't do QQ plots.