Pic2, the cumulative distribution function and quantile plot

Defination:

Cumulative distribution function: the cumulative distribution function (CDF) does just that. The CDF at point X tells us what
Fraction of events has occurred "to the left" of X. In other words, the CDF is the fraction
All points XI with Xi ≤ x.

Http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.cumfreq.html#scipy.stats.cumfreq

# -*- coding: utf-8 -*-"""Created on Thu Oct 23 20:29:33 2014@author: dell"""from scipy import statsimport matplotlib.pyplot as pltimport numpy as npimport randomif __name__ == ‘__main__‘:    ax1 = plt.subplot(211)    x = [random.gauss(0, 1) for i in range(1000)]    #res = stats.probplot(x, plot=plt)    mylist = stats.cumfreq(x, numbins = 100)    ax1.plot(mylist[0])        ax2 = plt.subplot(212)    mylist1 = stats.cumfreq(x, numbins = 100, defaultreallimits = [0,1])    ax2.plot(mylist1[0])    plt.show()

Defaultreallimits still does not quite understand what the definition is.

 

Bitmap: A Quantile plot is just the plot of a CDF in which the X and Y axes have been switched.

 

Probability diagram: the inverse function of probability plot Gaussian distribution will fall into the same line.

Http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.probplot.html

# -*- coding: utf-8 -*-"""Created on Thu Oct 23 20:06:03 2014@author: dell"""from scipy import statsimport matplotlib.pyplot as pltimport numpy as npimport randomif __name__ == ‘__main__‘:    nsample = 100    np.random.seed(7654321)        #A t distribution with small degrees of freedom:    ax = plt.subplot(321)    x = stats.t.rvs(3, size=nsample)    res = stats.probplot(x, plot=plt)        #A t distribution with larger degrees of freedom:        ax2 = plt.subplot(322)    x = stats.t.rvs(25, size=nsample)    res = stats.probplot(x, plot=plt)        #A mixture of two normal distributions with broadcasting:    ax3 = plt.subplot(323)    x = stats.norm.rvs(loc=[0,5], scale=[1,1.5], size=(nsample/2.,2)).ravel()    res = stats.probplot(x, plot=plt)        #A standard normal distribution:    ax4 = plt.subplot(324)    x = stats.norm.rvs(loc=0, scale=1, size=nsample)    res = stats.probplot(x, plot=plt)        # my test     ax5 = plt.subplot(325)    x = [random.gauss(0, 1) for i in range(100)]    res = stats.probplot(x, plot=plt)        #my test    ax6 = plt.subplot(326)    x = np.random.rand(100) * 100    res = stats.probplot(x, plot=plt)    plt.show()

 

Pic2, the cumulative distribution function and quantile plot