from numpy import *
from matplotlib.pyplot import *
from mpl_toolkits.axes_grid.axislines import SubplotZero
 
e = lambda mu,s,x: exp( (mu-x)/s )
pdf = lambda mu,s,x: e(mu,s,x) / ( s* (1.+e(mu,s,x) )**2 )

fig = figure(figsize=(6,5))
ax = SubplotZero(fig,111)
fig.add_subplot(ax)
 
ax.grid(True)
ax.minorticks_on()
 
x = linspace(-5,20,100)
mu = [5,9,9,6,2]
s = [2,3,4,2,1]
for b in arange(5):
	ax.plot(x,pdf(mu[b],s[b],x),lw=1.5,label=r'$\mu=%d,\, s=%d$'%(mu[b],s[b]))#'$c={}^1\!/_2$')

ax.set_ylim(0,.3)
ax.set_xlim(-5,20)
ax.legend(loc='upper right',frameon=False)
ax.set_yticks(arange(0,.4,.1))

fig.savefig("Logisticpdfunction.svg",bbox_inches="tight",pad_inches=.15)