from scipy.special import erf
from numpy import *
from matplotlib.pyplot import *
cdf = lambda a,x: erf(x/(a*sqrt(2.))) - (x*exp(-x*x/(2*a*a))*sqrt(2/pi)/a)
fig = figure(figsize=(5,5))
ax = fig.add_subplot(111)
ax.grid(True)
ax.minorticks_on()
x = linspace(.001,20,150)
ax.plot(x,cdf(1,x),label=r"a=1",linewidth=2)
ax.plot(x,cdf(2,x),'r',label=r"a=2",linewidth=2)
ax.plot(x,cdf(5,x),'g',label=r"a=5",linewidth=2)
ax.set_ylim(0,1.05)
ax.set_xlim(0,20)
ax.set_xlabel(r'x')
ax.set_ylabel(r'CDF')
ax.legend(loc=4)
fig.savefig("Maxwell-Boltzmann_distribution_cdf.svg",bbox_inches="tight",pad_inches=.15)